"Come on Over Baby (All I Want Is You)" was well received by most critics.
Billboard's Mia Nazareno called the song a "Radio Disney-approved bop" and complimented its "addictive", "danceable" sound. Chris Malone, also from the
Billboard magazine, noted that it was the singer's "first song where she was given significant creative control", and compared it to
Whitney Houston's early recordings. He added: "It's pure, unadulterated, feel-good pop, and stands as a shining example of why Aguilera has been able to achieve so much success."
UKMix named it "an upbeat, funky extravaganza, showing her [Aguilera's] voice off to the max". In 2005, "Come on Over Baby" was listed in the book titled
The 7,500 Most Important Songs of the Rock and Roll Era: 1944–2000 by Bruce Pollock, where the author called Aguilera "the voice of a new generation".
CDNow senior editor Eliseo Cardona wrote about Spanish version: "Indeed, the overly literal Spanish lyrics make for both a good laugh and a better yawn. This point is unwittingly made on 'Ven conmigo (Solamente tú),' the translation of 'Come on Over (All I Want Is You)'. If Spanish pop seems to make no sense at times, then this takes nonsense to the next level." A complete opposite opinion came from
Wall of Sound editor Kurt B. Reighley; to him it sounds "especially sassy en Español." Parry Gettelman of
Orlando Sentinel praised the vocals calling them "out-of-my-way."
Sun-Sentinel music writer Sean Piccoli wrote: "Ven Conmigo (Come with Me) borrows its bounce from the better
Whitney–
Mariah numbers." In August 2020,
Billboard named the song one of the "best 2000's Latin hits". It has been called "one of Aguilera's greatest hits" by
Rolling Stone en Español. Jamie Tabberer from the
Attitude magazine ranked "Come on Over Baby" at number ten on the list of Aguilera's seventeen best songs ever, Nicole Hogsett of
Yahoo! placed it at number six on a similar list, Similarly,
PopMatters editor Kimberley Hill praised the song as a "glittering bubblegum number". ==Chart performance==