The former Lion joined Jones' Aviva Premiership newboys earlier this month after his contract with Cardiff Blues was terminated in April.
It is just the latest in string of clubs for Henson, who toured New Zealand with the Lions in 2005, but Jones insists he is ready to make the most out of his remaining years in rugby.
"Gav has had three or four years of messing around and not being serious about his rugby," said London Welsh head coach Jones.
"He has grown up and realises now he still has four or five years left in the game and he wants to give it his best shot. He is certainly training hard and enjoying himself.
"When someone has been in the game for as long as he has, he just needs a comfortable environment to come into and perform. We all appreciate the potential but potential doesn't earn you a living.
"All we can do is offer him an opportunity to come and enjoy his work and I'm sure the Aviva Premiership will benefit from having someone of his quality in the league."
Henson enjoyed some of his best rugby while playing under Jones at the Ospreys, where he won two Celtic titles and the Anglo-Welsh Cup.
And Jones is confident that Henson can flourish at the top level once again after being handed the Exiles' No.10 jersey.
"I don't know why he lost his way and I don't care," added Jones.
"What's happened has happened and now it's all about the future and moving forward.
"We're not asking a great deal of him. He has had a difficult 18 months so he just needs to come in and settle down, which is what he's doing.
"Looking at him play in the past, he has the ability to control the game for us and be a decision maker on the pitch."