The 26-year-old former Southampton centre-back joined the Glovers in the summer and has made 11 appearances for the Championship side this season but the most recent of those came when he conceded a penalty in a 2-1 loss to Leicester on October 1.
Seaborne will remain with the Sky Blues until January 5 and becomes the second arrival ahead of the loan deadline after Barnsley striker Chris Dagnall.
City boss Steven Pressley said: "Danny has the ability to be a strong and imposing figure in the heart of the back four and I'm delighted we've been able to bring a player of his calibre to the club.
"We tried to bring him in in the summer but circumstances and the offer of Championship football meant we couldn't quite get a deal done however I'm delighted we now have him on board.
"Our players have been working exceptionally hard this season but because of the relatively small depth to our squad the players will certainly welcome his addition and experience."