The Premier League leaders had identified the 34-year-old as the ideal back-up for Thibaut Courtois in case Asmir Begovic left for Bournemouth, but Chelsea had two bids knocked back by Celtic.
Gordon has now made the decision to commit his long-term future to Celtic instead and will stay put for an additional three seasons.
"It has taken a little while after the interest in the January window but it is good to finally get it done and concentrate on the rest of the season," Gordon said.
Hoops No.1 Craig Gordon has committed himself to the club by signing a new three-year deal keeping him at Celtic Park until 2020. pic.twitter.com/KIktVsklSN— Celtic Football Club (@celticfc) March 8, 2017
"It was quite stop-start, there was a lot of things going on within the club, it was not a continuous thing, it was not like we were talking about it for months. There were two or three occasions when we sat down and talked about it, it was fairly straightforward in the end, I wanted to stay.
"We have a big chance to go for another trophy before the end of the season and we are well ahead in the league, it is only a matter of time before we wrap that one up. We are looking good, we do not want to look too far in the future, we have got a lot to try and finish off this season, it is a very exciting time.
"It has been a good season, the team have been playing really well domestically, we have won every match since I have been back in the team, you cannot really ask for a lot more than that."
Gordon joined Celtic from Sunderland in 2014 and has since developed into a key figure at the Scottish champion, keeping an impressive 22 clean sheets this season.