Barzani was elected during a parliamentary session on Tuesday where he won a total of 68 votes from the 81 lawmakers attending the session.
"Congratulations to the new President of the Iraqi Kurdistan Region PMBarzani," Bolton wrote on Twitter.
He further praised the political move and considered it a significant one.
"A significant milestone for the Kurdistan Regional Government, a steadfast U.S. ally in the Middle East."
The new Kurdish president is expected to take oath during his inauguration on 10th June, Kurdistan Region Parliament said in a statement.