Aldred, who counts Carlisle and Watford among his former clubs, was released by the U's earlier this month and recently began training with Leam Richardson's Stanley squad
"I think this has been in the pipeline for the last couple of weeks so it's been good to get it all finalised and done," the 22-year-old said in an Accrington club statement.
"I'm just looking to hit the ground running, get myself up and running and get into the team. Hopefully I can establish myself and make a name for myself here."
"I know quite a lot about Tom," said Richardson of the former Scotland Under-19 international.
"He's a good defender and potentially he could be very, very good. I've been very pleased with how he's come in and applied himself and I think he has some great attributes which I think we lack.
"He's very powerful and he likes defending so he adds to what we have in the defensive area."
Earlier on a busy transfer deadline day, Accrington brought in goalkeeper Paul Rachubka and defender Mark Hughes on loan from Leeds and Bury respectively while extending Nicky Hunt's stay from Rotherham.
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