Vázquez signed with Major League Soccer expansion club Atlanta United in December 2016 ahead of their inaugural season.

[3] On April 22, 2017, Vázquez played in his first competitive MLS match, coming on as a substitute against Real Salt Lake and scoring a goal in the final minute of stoppage time.

[4][5] In his first two seasons with the club, under manager Tata Martino, Vázquez was deployed as a winger rather than his natural position of leading the line as a striker.

As a reserve, Vázquez made 21 appearances and scored one goal over those two seasons, culminating with Atlanta winning the MLS Cup title in 2018.

[11] On August 3, Vázquez was selected for the 2022 MLS All-Star game as a replacement for striker Valentín Castellanos who was loaned by NYCFC to LaLiga side Girona FC after making the original 2022 roster.

On January 6, 2025, Vázquez returned to the United States, joining Austin FC on a four-year deal for a club record transfer fee.

"[33] Vázquez made his senior debut and start in an international friendly match against Serbia on January 25, 2023, at BMO Stadium in Los Angeles.

In his first ever Gold Cup knockout stage match, Vazquez scored an 88th minute go-ahead headed goal versus Canada.