Much as he did at Carrow Road under David Marshall, Nelson, 27, will provide cover for Jamie Langfield, the current Dons Number One.
Nelson was released despite Marshall's transfer to Cardiff at the start of the summer. City boss Bryan Gunn has entrusted promising youngsters Declan Rudd and Jed Steer with backing up new first choice Michael Theoklitos.
Ben Alnwick has also joined on loan from Tottenham and impressed against Manchester United XI on Saturday, saving a first half penalty.