"I am willing to wage a hard-fought campaign for the opportunity to continue Dr. Coburn's conservative legacy," Lankford said in a statement, calling Coburn a friend and role model.
In his statement, Lankford also took a few digs at Senate Democrats, Politico reported.
"The Senate is the most contentious body in our government today. Harry Reid and the Senate Democrats continue to divide America for political gain," Lankford said.
The Senate Conservatives Fund announced it would not support Lankford because conservatives "cannot count on him to fight for their principles."
"We won't support Congressman Lankford's bid for the Senate because of his past votes to increase the debt limit, raise taxes, and fund Obamacare," Senate Conservative Fund Executive Director Matt Hoskins said in a statement.
GOP Rep. Tom Cole said Sunday he would not run to complete Coburn's unexpired term.
Coburn, a medical doctor and staunch fiscal conservative, announced last week he would retire at the end of the current congressional session, two years before his term is complete. The Oklahoma Republican told Politico recently his recurrence of prostate cancer could force him to leave office early, but his announcement Thursday said his health was not why he was retiring.
"As a citizen, I am now convinced that I can best serve my own children and grandchildren by shifting my focus elsewhere," he said. "In the meantime, I look forward to finishing this year strong."