Johnson, who missed the majority of last season with a knee injury, was granted permission to speak to the Barclays Premier League newcomers during the final hours of the transfer window on Monday night.
The 32-year-old arrived at the Eagles' training ground but, when it became apparent Rangers were unable to sign another striker as a replacement, a deal could not be reached before the 11pm deadline.
However, Johnson is adamant he will give his all for QPR this season as they bid for promotion from the Sky Bet Championship and an automatic return to the top flight.
He told the club's official website, qpr.co.uk: "It was a bit of a whirlwind last night, but I'm really pleased to still be a QPR player.
"The interest from Palace was flattering but I never once asked for a transfer. Like I said a few weeks back I owe it to QPR, who stood by me when I was injured last season, to stay and help get this club back to the Premier League.
"I am one hundred per-cent committed to QPR and will continue to give my all to help us build on what has been a promising start to the season."
Rangers boss Harry Redknapp added: "We reluctantly gave Andy the chance to speak to Palace, who are a club close to his heart. They were keen to offer him a two or three-year deal and we felt we couldn't hold him back from at least talking to them.
"However, when it became apparent we weren't going to be able to get sufficient cover in ourselves in that department before the deadline, we knew we couldn't let Andy go.
"Andy has been great for us in the opening month of the season and remains a key player for us.
"He's committed and looking forward to the challenge of helping us challenge for a return to the Premier League."
Johnson remains a popular figure at Palace, having scored 74 goals in 140 league appearances during a four-year spell at Selhurst Park between 2002 and 2006.