Coats, an Indiana Republican, served as a senator from 1989 to 1999, and again from 2011 to 2017. He served eight years in the House of Representatives.
Coats met with Trump at the end of November at Trump Tower. The retired senator told reporters at the time that he was "not seeking a specific position" but went to offer advice, according to the Indianapolis star. Coats said in March 2015 that he would retire from the Senate when his term ended at the start of this year.
The announcement comes as the president-elect has criticized American intelligence agencies.
Trump has expressed doubts about Russia's involvement in the U.S. presidential election. He played down the ramifications of any Russian interference and said, it's "time for the country to move on to bigger and better things."
On Thursday, James Clapper, the head of the U.S. intelligence told a Senate committee that Russia poses "an existential threat to the United States." But Clapper also said the Russian hacking efforts "did not change the vote tallies" in the election.
The former senator will need to win confirmation by the Senate.
—NBC News contributed to this report.