The songs first debuted on iTunes Wednesday, then were made available through all digital outlets Thursday.
An iTunes Pass for Allen has been established and features a download of his version of "No Boundaries." His debut album will also be made available on iTunes when released, as will exclusive music and video content through the coming months, his record label 19 Entertainment said.
Written by "American Idol" Judge Kara DioGuardi, Cathy Dennis and Mitch Allan and produced by Eman, "No Boundaries" was performed by both contestants on "American Idol" on both the Tuesday night performance show, as well as the Wednesday night finale, in which Allen was declared the winner.
Allen and Lambert, along with the rest of the top 10 "American Idol" contestants, are set to go on tour this summer, starting July 5 in Portland, Ore.