Button has been managed by Richard Goddard for some time in his Formula One career, and the two have become firm friends.
After Di Resta split from Anthony Hamilton in early July, with the issue to go to the High Court, he has been in limbo for the last two months at an important time with the driver merry-go-round poised to start up.
The Scot has had Goddard's Sports Partnership in the background of late, almost as a trial run to explore whether they could work together, and a deal was confirmed on Saturday following qualifying for the Italian Grand Prix at Monza.
Speaking to Press Association Sport about the move, Di Resta said: "I've clearly been impressed so far.
"I'm hoping it's a strong relationship and we will work together and do bigger and better things.
"There are plenty of opportunities out there, and although it is early days, I believe we'll see the benefits over the next couple of months.
"But having seen what he has done for Jenson, and what the whole pit lane says about the way he works, it was a big thing.
"He's in the background, he does the right things, he's genuine, and it's a good point in my life for me to get good direction and work on something for the years to come."
The appointment of Goddard, who is assisted by James Williamson these days, now leaves Di Resta free to focus on his driving whilst they look at the options available for next year and beyond.
Di Resta has been linked of late to Mercedes and McLaren should Michael Schumacher and Lewis Hamilton move on.
"There are plenty of offers around," said Di Resta.
"Being without a manager has not really affected my on-track performance anyway, and you probably won't see the true benefits of this relationship until next year and until they get some time to see who I am and what I'm about.
"But I know they'll take the necessary involvement, the way they want to do it and the way I want to do it, and hopefully they will take the stress off me in certain areas."
Di Resta at least produced a strong performance over the weekend in Monza after a recent poor run in which he collected just one point from the last four races.
The 26-year-old conjured the best qualifying performance of his career on Saturday of fourth, only to start ninth due to a gearbox change and five-place grid penalty.
Finishing eighth was as good as Di Resta could have hoped for, adding: "We're happy enough going away with the points we've got.
"The only downside is the points (Sergio) Perez has scored (18 for second), but the Sauber was in a different world by the looks of it with how quick he was.
"But we will take the positives from the weekend, analyse things and try and improve our race pace in time for Singapore."