Thompson, who was released by City after the end of last season, has remained in Sky Bet League 1 after signing a one-year deal with Notts County.
Fresh from leaving the Coral Windows Stadium on Tuesday, McLaughlin has joined League 2 club Burton Albion for the 2014/2015 campaign. McLaughlin has also penned a one-year deal.
Thompson and McLaughlin become the fourth and fifth players to find new clubs from the group of players who finished last season for City.
Defenders Matthew Bates and Carl McHugh joined Hartlepool United and Plymouth Argyle respectively this summer, while winger Kyel Reid left for Preston North End.
In return, City have brought six new players into the Coral Windows Stadium over the last couple of months - Matthew Dolan, Billy Knott, Gary Liddle, Alan Sheehan, Billy Clarke and Jordan Pickford.