Barcelona attempted to sign the 23-year-old in the summer transfer window but were unable to agree a deal with the French champions.
With the deal reported to be for five years, Klopp hailed Henderson's contribution under his management.
Rhian Brewster has not suffered an injury setback as a report from the Mirror had indicated on Wednesday night as the Liverpool Echo claim he was never likely to return to action until after Christmas.
Henderson told Liverpool's club's website: "I'm very happy to have signed a new contract for a long period of time". The German manager said, "Jordan embodies entirely what it means to be a Liverpool player in this modern era of football".
"Everybody should know we have a lot of work to do still, but if they don't then I have told them".
"I'm so impressed with Gomez, the balance of the team is so much better now, with so much pace, they can defend one-versus-one, because at times they are going to have to".
Despite having missed out on a place in Didier Deschamps' FIFA World Cup-winning side this summer, the midfielder is an impressive physical player with impeccable technical abilities. I want to be here for as long as I can be. "He is our "General" and I trust him completely". Henderson has made 283 appearances in all competitions for Liverpool, scoring 24 goals in the process.
"We have held positive discussions with government about the importance of access to European players for our clubs, and the many cultural and economic benefits a globally popular Premier League brings to the United Kingdom".