Quayle plans to announce his support for the former Massachusetts governor Tuesday afternoon at an event in Paradise Valley, Ariz., where Quayle has a home.
Quayle served as vice president under President George H.W. Bush. He was a House member from Indiana for two terms and a U.S. senator.
Quayle has largely stayed out of the national political spotlight in recent years, though he did mount an unsuccessful presidential bid in 2000. A series of gaffes during his vice presidency made him the subject of late night comedians' punch lines.
His endorsement helps illustrate establishment GOP backing for Romney, who has been trying to consolidate support among party stalwarts despite repeated challenges from conservative alternatives. The latest, former House Speaker Newt Gingrich, has been leading in polls both nationally and in critical early states.
Quayle served under Bush, who met with Romney last week at his Houston home. The elder Bush did not offer his endorsement.
Quayle's son, Rep. Ben Quayle, was elected to the House of Representatives in 2010.
A GOP official familiar with Quayle's thinking says the former vice president is backing Romney because he views Romney as the most credible candidate in the race. The official requested anonymity to discuss Quayle's endorsement ahead of the official announcement.