Former Force India driver Di Resta sacked Hamilton as his manager in 2012 following a dispute over an apparently lucrative sponsorship deal with energy drinks company Go Fast.
In return, Hamilton sued Di Resta for breach of contract and loss of earnings, resulting in an acrimonious High Court hearing in December.
Di Resta has also since lost his seat with Force India, and instead will again compete in German touring car series DTM, a championship he won with Mercedes in 2010.
A statement issued by Di Resta's current management company, The Sports Partnership, confirmed the battle with Hamilton has now been brought to a close.
Suggesting regret over the public spat with Di Resta, Hamilton said: "I am very sorry Paul and I fell out to the extent we did, and I am pleased to put this matter to bed.
"Paul is a very talented driver, and it is a real shame he does not have the F1 seat in 2014 he deserves.
"I am sure he will do fantastically well in DTM for Mercedes, and I wish Paul the very best for the future."
Scot Di Resta kept his remarks brief as he now looks to rebuild his motor racing career away from Formula One.
The 27-year-old said: "This has been a difficult year, and I am just pleased to put it behind me and to concentrate on my racing.
"I am looking forward to racing in DTM for Mercedes this year and to the future ahead."