President Sheikh Mohamed and Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, sent messages of support to Mr Rashid, who was sworn in on Thursday.
Mr Rashid, a former water resources minister, was voted in to power by Iraq's Parliament in what is considered a significant step towards ending political deadlock spanning more than a year.
Iraq's politicians have been unable agree on forming a government since Parliamentary elections in October 2021.
The new president named Mohammed Shia Al Sudani as prime minister.
Mr Rashid, 78, is a veteran politician, having previously served in high positions of government.
Born in the northern city of Sulaymaniyah, in the Iraqi Kurdish region, he began his political career in his 20s, after joining the Patriotic Union of Kurdistan party.
Mr Rashid achieved his degree in civil engineering from the University of Liverpool in the UK and continued his education there, earning a master's degree and a doctorate in engineering from the University of Manchester.
He served as Iraq's minister of water resources from 2003 to 2010, before being appointed as a senior adviser in the PUK by the late president Jalal Talabani, who was founder of the group and Mr Rashid's brother-in-law.