What is the biblical basis for the Covenant of Redemption? In Covenant Theology the Covenant of Redemption is an eternal agreement made between the members of the Trinity in which the Son of God agrees to become incarnate and die for the the sins of God's people. In return the Father promises to raise the Son back to life and glorify him.

What is the biblical basis for this idea? Answers do not have to show that the Bible uses the term 'covenant' to talk about this, but should show that this agreement was made before time began.
The Covenant of Redemption in the Bible


  Your attitude should be the same as that of Christ Jesus: Who, being
  in very nature God, did not consider equality with God something to be
  grasped, but made himself nothing, taking the very nature of a
  servant, being made in human likeness. And being found in appearance
  as a man, he humbled himself and became obedient to death-- even death
  on a cross! Therefore God exalted him to the highest place and gave
  him the name that is above every name, that at the name of Jesus every
  knee should bow, in heaven and on earth and under the earth,  and
  every tongue confess that Jesus Christ is Lord, to the glory of God
  the Father.
  
  Philippians 2:5-11 (NIV)


Here we see the outworking of the Covenant of Redemption. Jesus humbled himself to "death on a cross" and "therefore God exalted him." We see the same sort of thing in John 17. Jesus brings the Father glory, therefore the Father will bring him glory:


  I have brought you glory on earth by finishing the work you gave me to
  do. And now, Father, glorify me in your presence with the glory I had
  with you before the world began.
  
  John 17:4-5 (NIV)


Jesus says these sorts of things all throughout John. It's also in Isaiah 53:


  Yet it was the LORD's will to crush him and cause him to suffer, and
  though the LORD makes his life a guilt offering, he will see his
  offspring and prolong his days, and the will of the LORD will prosper
  in his hand. After the suffering of his soul, he will see the light
  [of life] and be satisfied; by his knowledge my righteous servant will
  justify many, and he will bear their iniquities. Therefore I will give
  him a portion among the great, and he will divide the spoils with the
  strong, because he poured out his life unto death, and was numbered
  with the transgressors. For he bore the sin of many, and made
  intercession for the transgressors.
  
  Isaiah 53:10-12 (NIV)


Psalm 2* speaks of the glory given to Christ as decreed by the Father:


  I will proclaim the decree of the LORD: He said to me, "You are my
  Son; today I have become your Father. Ask of me, and I will make the
  nations your inheritance, the ends of the earth your possession. You
  will rule them with an iron scepter; you will dash them to pieces like
  pottery." Therefore, you kings, be wise; be warned, you rulers of the
  earth. Serve the LORD with fear and rejoice with trembling. Kiss the
  Son, lest he be angry and you be destroyed in your way, for his wrath
  can flare up in a moment. Blessed are all who take refuge in him.
  
  Psalm 2:7-12 (NIV)


Before time began

But when was this agreement made? If it's spoken of by David and Isaiah, it's at least as old as the time of David. But was it made before time began? The reformed say yes. R.C. Sproul articulates the reformed position this way:


  The Bible speaks often of God’s eternal counsel, of His plan of
  salvation and the like. It is a matter of theological urgency that
  Christians not think of God as a ruler who ad libs His dominion of the
  universe. God does not “make it up as He goes along.” Nor must He be
  viewed as a bumbling administrator who is so inept in His planning
  that His blueprint for redemption must be endlessly subject to
  revision according to the actions of men. The God of Scripture has no
  “plan b” or “plan c.” His “plan a” is from everlasting to everlasting.
  It is both perfect and unchangeable as it rests on God’s eternal
  character, which is among other things, holy, omniscient, and
  immutable. God’s eternal plan is not revised because of moral
  imperfections within it that must be purified. His plan was not
  corrected or amended because He gained new knowledge that He lacked at
  the beginning. God’s plan never changes because He never changes and
  because perfection admits to no degrees and cannot be improved upon.


Are there verses to support this idea? Yes. In 2 Timothy, Paul says that God saved us by giving us grace in Christ Jesus "before the beginning of time"**:


  So do not be ashamed of the testimony about our Lord or of me his
  prisoner. Rather, join with me in suffering for the gospel, by the
  power of God. He has saved us and called us to a holy life—not because
  of anything we have done but because of his own purpose and grace.
  This grace was given us in Christ Jesus before the beginning of time,
  but it has now been revealed through the appearing of our Savior,
  Christ Jesus, who has destroyed death and has brought life and
  immortality to light through the gospel.
  
  2 Timothy 1:8-10 (NIV)


Lastly, Ephesians 1 brings together all the themes previously discussed. We see God purposing to reveal the mystery of his will to us "before the creation of the world" by bringing all things together "under Christ."


  Praise be to the God and Father of our Lord Jesus Christ, who has
  blessed us in the heavenly realms with every spiritual blessing in
  Christ. For he chose us in him before the creation of the world to be
  holy and blameless in his sight. In love he predestined us for
  adoption to sonship through Jesus Christ, in accordance with his
  pleasure and will— to the praise of his glorious grace, which he has
  freely given us in the One he loves. In him we have redemption through
  his blood, the forgiveness of sins, in accordance with the riches of
  God’s grace that he lavished on us. With all wisdom and understanding,
  he made known to us the mystery of his will according to his good
  pleasure, which he purposed in Christ, to be put into effect when the
  times reach their fulfillment—to bring unity to all things in heaven
  and on earth under Christ.
  
  Ephesians 1:3-10 (NIV)


Additional Resources


Of Christ the Mediator | Westminster Confession***
The Covenant of Redemption between the Father and the Redeemer | John Flavel (1627-1691)
What Is the Covenant of Redemption? | Ligonier Ministries
Is there a biblical basis for the Covenant of Redemption? | Monergism.com




* Psalm 2 is considered a messianic psalm in the Christian tradition, especially by the reformed, and it seems hard to argue against that given the way it's used in Hebrews 1.

** I almost included Revelation 13:8 at this point. The verse was discussed on BH.SE and this translation was suggested: "All those who live on the earth worshiped it, anyone whose name has not been written in the scroll of life (which belongs to the slain Lamb) since the world's founding." The more traditional "lamb who was slain from the foundation of the world" would be a more convincing addition to this post, but I think even the translation given by Mark Edward works to support the point. After all, names were written in the scroll of life since the world's founding, and their being there depends on the lamb being slain. Hence the names must have been written before the foundation of the world with the knowledge of Christ's future sacrifice.

*** B. B. Warfield called covenant theology the "architectronic principle" of the Westminster Confession, but it's not universally agreed that it teaches the Covenant of Redemption. Chapter 8: Of Christ the Mediator is cited by those who believe it supports the concept. Very few would dispute that it supports the Covenant of Grace or Covenant of Works, however.

Addendum: The Covenant of Redemption is really threefold. The question captured two of its aspects, that of the Son dying and Father glorifying him, but equally important is the Father's promise to send the Spirit. This answer focused on the aspects that the question did, but if you want to understand the Covenant of Redemption, it's important to note the sending of the Spirit.