If Christ took our sins on him, why do we still need an imputation of God's righteousness on us? I always thought that the imputation of our sins on Jesus so that we are free from sin is what justified us. But according to several passages in the Bible (What is the biblical basis for the imputation of Christ&#39;s righteousness to believers?) there is also an imputation of God's righteousness onto us.

It seems strange to me that the imputation of our sins on Christ isn't enough to make us righteous before God, but that we would still need an imputation of God's righteousness on us despite our sins having been washed away.
Are these actually two separate acts or are they identical?
The words ‘righteousness of Christ’ never occur in scripture. What does occur is ‘the righteousness of God’ And that is the answer to your question - why if sins were borne by Christ , do we still need an ‘imputation’ ? That is a very intelligent question; very valid.

The righteousness of God is revealed in the gospel, Romans 1:17. It is revealed at Golgotha. It is revealed when God drew near and resolved all righteousness in the sufferings and death and bloodshed of Jesus Christ, his own beloved Son. 

Jesus Christ bore the sins of others, in his body, on the tree, I Peter 2:24. And Jesus Christ was made sin - sin, as such, the thing itself  was contained within him, unto death, II Corinthians 5:21. When he died, it was taken away. Behold the Lamb of God which taketh away the sin of the world, John 1:29.

When one believes this gospel, sees and believes that God’s own righteousness was met and satisfied in Jesus Christ himself as he suffered and died - then God sees that faith and sees, within that faith, his own righteousness.

The righteousness of God is seen within the faith of the believer. And God, seeing that faith, seeing his own righteousness reflected in that faith - God accounts that person to be right. For he is right. He is right to believe that he is a sinner. And he is right to believe in Jesus Christ. And he is right to see that God’s rightness was fully met and satisfied within Christ.

This is a massively important subject. This is the heart of the gospel. 
The gospel reveals this. Nothing else does. 

And I am not ashamed of this gospel; for therein is the righteousness of God revealed - out of faith - unto faith. Romans 1:16.