Kirk, a former aide and longtime Kennedy friend, will give President Obama the critical 60th U.S. Senate vote he needs to pass a health care overhaul this year.
Kirk said in accepting the appointment that he will not run for the seat in January. Patrick and Sen. John Kerry, D-Mass., gave the same assurance -- saying Kirk is acting as a "caretaker appointment."
"This appointment is a profound honor. I accept it with sincere humility," Kirk said. He is expected to be sworn in Friday afternoon.
Patrick said Kirk would carry on Kennedy's work. Obama, in a written statement, praised the decision.
"Paul Kirk is a distinguished leader, whose long collaboration with Senator Kennedy makes him an excellent, interim choice to carry on his work until the voters make their choice in January," Obama said.
But the National Republican Senatorial Committee called the appointment nothing more than a "power play" aimed at forcing through health care legislation.
"The Democrats' power play in Massachusetts has nothing to do with principle, and everything to do with politics. With their unpopular government-run health care bill on the brink of failure, Democrats in Washington desperately need another vote in the U.S. Senate, and it is clear that this administration will stop at nothing to ram it through the Congress," reads a written statement from Rob Jesmer, executive director of the NRSC.
Kirk had the backing of the Kennedy family, which released a statement Thursday saying the governor "could not have selected a more outstanding person" to succeed Kennedy.
"With today's appointment of Paul Kirk, the people of Massachusetts will once again have two voices and two votes in the United States Senate, fighting for them each and every day on the issues they care about," the family said.
The appointment comes after the Massachusetts Legislature approved a bill allowing the governor to name a successor to Kennedy, who died last month after a yearlong battle with brain cancer.
Patrick had said Wednesday he would send a letter to the secretary of state to declare an emergency that would allow him to override a legislative vote that defeated his administration's effort to make the bill take effect immediately. Normally, legislation faces a 90-day waiting period.
The 71-year-old Kirk, a Boston attorney, was close friends with the senator. He and his wife, Gail, live on Cape Cod, and he was among the few regular visitors allowed at Kennedy's Hyannis Port home before he succumbed to brain cancer Aug. 25.
The Associated Press contributed to this report.