Clarke, 46, was chosen by a five-man selection panel ahead of Jimenez and Thomas Bjorn of Denmark on Wednesday.
Although feeling "a little disappointed", Jimenez has made himself available to assist Clarke at Hazeltine, United States.
"I sent Darren a text last night just to say well done and that I know he'll do a great job," said the 51-year-old.
"I didn't call him because I knew he would be very busy but I wanted to say well done and that if he needs anything from me when he is captain then all he has to do is call me.
"He deserves to be the Ryder Cup captain as much as I do. I would love to do it one day but I am happy for Darren because he has done a lot for the Tour as well."
Clarke succeeds Irishman Paul McGinley, who led Europe to a five-point victory over the USA at Gleneagles, Scotland in 2014.
While Clarke has struggled with his game in recent seasons, Jimenez is still competing on the European Tour and has also been winning titles on the Seniors Tour.
Jimenez has played in four Ryder Cups winning twice, and been victorious on each occasion he has been vice-captain, in 1997, 2012 and 2014.
He added: "To me the Ryder Cup is very important and I will always want to be involved in it in some way. I suppose the best way for me to be involved is by taking my clubs. You never know - maybe you will see me at the next one with my clubs."
The 2000 US Open runner-up added on Sky Sports: "It's disappointing a little bit. I've been there for so many years on Tour, this is my 27th season, played several Ryder Cups and been vice-captain in some other ones."
Meanwhile, Davis Love III, 50, is expected to be confirmed as captain of the United States Ryder Cup team on 24 February, four years after he led the side to defeat at Medina.
The memorable European win under Jose Maria Olazabal in 2012 became known as the Miracle of Medina after Europe fought back from 10-6 down going into the final day's singles to win 14½-13½ on US soil.
Ted Bishop, the former president of the Professional Golfers' Association, says he would choose Fred Couples as the next US Ryder Cup captain.
Europe's Ian Poulter claims that while being Europe's captain is a coveted role, its US counterpart is less prestigious.
He told BBC Radio 5 live: "It's not a role that many people want to put their hands up for. They haven't had a lot of success over the last decade or so and that's a difficult role.
"It was very difficult for Davis at Medina, he basically had nearly 10 fingers holding that trophy on the Saturday and thankfully for team Europe we managed to pull it out his hands. That must be very painful for him."