Sinema has sided with the president on more than 50 percent of votes held in the Senate.
"Kyrsten Sinema won because she ran a good race and had a message that resonated with Arizona's voters," Flake said.
Outgoing GOP congresswoman is chosen by the state's governor to serve the remaining two years of John McCain's term.
Arizona's senator-elect called on lawmakers to follow the example of the late Senator John McCain, recalling his words: "But we have always had so much more in common with each other than in disagreement."
Voters elected the country's first Muslim and Native American women to Congress, in addition to a number of other firsts.
"It was OK for Americans to join the Taliban to fight against us," McSally said.
Former GOP communications director Tara Setmayer said Joe Arpaio's Senate run could be "Roy Moore part two."