The 31-year-old had a meeting with Allan Moore on Tuesday, in which the Ton boss intimated his desire to retain the versatile Englishman's services for what will be his 10th season with the club.
Following that initial discussion, Weatherson thrashed out the terms of a new contract with chairman Douglas Rae before signing this afternoon.
Afterwards, Weatherson told the Tele: "I've signed the paperwork on a one-year contract after agreeing terms on Tuesday.
"I really wanted to stay here at Morton, so I'm absolutely delighted to have been offered a new deal with the club."
Weatherson is due to receive a testimonial match next summer.