Crouch linked up with Sean Dyche's side after Burnley agreed to swap Wales striker Sam Wolves for the 6ft 7in (201cm) former Liverpool and Tottenham star.
The 38-year-old has scored 108 goals in 462 top-flight games throughout his career.
He has joined Burnley on a short-term deal until the end of the season, with manager Sean Dyche hoping the veteran can provide an extra boost in the battle against relegation.
Crouch has played 23 times in the Championship this season, starting only twice and scoring once.
He also scored against Shrewsbury in the FA Cup third round.
Only 23 players have scored more than Crouch's 108 goals since the inception of the Premier League in 1992 -- he just needs four more to climb into the top 20.
"I still want to achieve things. I want to get more games in the Premier League and I would love to add to the 100 Premier League goals," Crouch said.
"If I can add to that and get up the list that would be great as well, and hopefully that will all cumulate in Burnley moving forward.
"It's a club that is stable in the Premier League now. We've got to make sure we stay there this year and build on that.
"I know I can impact games at this level. I scored goals last season in the Premier League and I know I will do the same again if given the opportunity this year."
Vokes, 29, who joined Burnley from Wolves in 2012, has signed a three-and-a-half-year deal with Stoke.