Released in the summer of 1996, it is commonly known among Ronstadt fans as 'The Lullaby Album'. It reached number 78 - and lasted three months - on the Billboard album chart. It also earned the singer a new career distinction when it hit #1 on the Top Kid Audio chart. It easily outsold Linda's previous several albums and was awarded a 1997 Grammy.
This album was reissued on Rhino's Flashback Records label in 2009.
Allmusic critic Stephen Thomas Erlewine rated the album 2.5 of 5 stars, writing: "All of the songs are given lush, sweet, and soft arrangements, even when that approach is ludicrous; it might be a cute idea to deliver Queen's "We Will Rock You" as a rock-a-bye chant, but in practice it is simply ridiculous… the appeal of Dedicated to the One I Love is limited..."