Iron chairman Peter Swann has wasted no time in raiding his former club for winger Hawkridge and center back Luke Waterfall.
Hawkridge has only been at The Northolme for a year, but the skilful 23-year-old is reported to have been tracked by Football League clubs for several months.
“Luke and Terry prove that we not only realise the need to sign experienced players to help us out of League Two but not to take our eye off potential local players that may prove to be excellent signings for the future,” said Swann, in a statement.
“Both Luke and Terry have attracted the interest of many a league club and we are delighted to offer this opportunity for them here at Scunthorpe.
“We wish them the best here at the club and believe the full time regime of league football will improve and get the best out of each of them.”
Both players have signed one-year deals at Glanford Park.
Although free agents, both Waterfall and Hawkridge had been offered new terms by Gainsborough and as they are under the age of 24, Trinity will be due compensation.