Harrad, 32, rejoins the Gulls after leaving Wrexham, subject to international clearance, having spent the second half of 2015-16 at Torquay.
He comes in to replace Nathan Blissett, who is set to move to Plymouth Argyle.
Reid, 22, who moved to Plainmoor on loan in the summer, has scored three times in 26 National League games.
"I was delighted to get the call and be here to help the club progress up the league table," Harrad told BBC Sport.
"I want to help us finish as high as possible, there are some talented players who came in here over the summer and we're looking to get some consistency into the performances to progress and get up that league table.
"The reason I've come back is that I'm wanted ,and as a player that's essential. Kevin (Nicholson, Torquay manager) knows what he's going to get from me and vice-versa and I think we have a good working relationship."
Nicholson commented: "His work-rate, what he brings off the pitch in terms of his leadership qualities, and how he is is as a man will be something that the lads can look up to."
On Reid's loan extension, Nicholson said he expects the forward to improve as the season goes on.
"It's great for him, great for Exeter to have a player playing regularly and it's great for us because he's shown in patches how good he is, but I think there's still a lot more to come," he added.
Find all the latest football transfers on our dedicated page.
Torquay United have signed striker Shaun Harrad and extended the loan of Exeter City forward Jamie Reid until the end of the season.