Weaver, who counts Manchester City, Charlton and Dundee United among his former clubs, left Sheffield Wednesday this summer.
The 34-year-old has signed a six-month deal at Pittodrie and will vie with Jamie Langfield for the goalkeeper's position in Derek McInnes' side.
Dons manager McInnes said that he was delighted to add the experience keeper to his group of players and said he had chosen the Englishman ahead of other possible new recruits.
"I'm delighted to get Nicky on board," he told Aberdeen's official website.
"To get such an experienced and talented goalkeeper is important and to get him during the pre-season stage is great for him in terms of being able to integrate with the boys.
"We had a few avenues and other options but we feel with the signing of Nicky we've recruited well and Nicky's eagerness and willingness to come here was pivotal."
Source: Manchester City MAD