Bamford, who spent last season on loan at Middlesbrough, has agreed the switch on the same day that it was announced he had signed a new three-year deal at Chelsea.
The 21-year-old won the Championship Player of the Year award for his efforts at Middlesbrough last season, scoring 17 goals as the Teessiders lost out in the play-off final to Norwich.
He told the Palace website: “I was quite keen to stay close to London this time and Palace were actually my first choice, but I didn’t realise they were keen to start with.
“Then, when I met with the manager (Alan Pardew), he put forward his plans and it was an easy decision.
“I do like to score goals, so hopefully I’ll be able to do that a lot here. I want to try to establish myself in a Premier League team and if I can do that here then it would be great for me and great for the club.”
The England U21 international has also spent time away from Stamford Bridge with temporary spells at MK Dons and Derby, having begun his career at the Nottingham Forest academy.
Regarding his new deal at Chelsea, he told their website: “I’m delighted to sign a new contract with Chelsea. My dream has always been to be part of this club for the long term.
“Chelsea have been fantastic with my development and joining Crystal Palace for this season on loan is the next step for me in my career.”
Palace manager Alan Pardew said: “It’s a coup for Crystal Palace ahead of a host of rivals. I’m so pleased he chose us over others to help develop his game. Hopefully he will be a star for us, Chelsea and – of course – England.”