Rondon scored 24 Premier League goals since joining the Baggies three years ago.
Ian Holloway's Palace will now go into their daunting trip to Manchester United in two weeks' time with three points on the board, while Paolo Di Canio's Sunderland have taken just one point from a possible nine.
Gayle, 22, joins Palace on a four-year contract after a season in which he scored 20 times for Peterborough and third-tier Dagenham and Redbridge, with whom he turned professional only 12 months ago. "I'm ecstatic really. I just want to get pre-season started now," Gayle told the Palace website.