The 31-year-old winger has linked up with the Northern Premier League club for an undisclosed fee.
Despite injuries to Jay Rollins and Joe Leesley, Hawkridge - who has previously played for Scunthorpe United, Nots County and Lincoln City with whom he won the National League title in 20-17 - has found himself further down the Pilgrims' pecking order following the summer arrival of Jordan Preston and impressive form of his brother Fraser.
Basford have also announced the arrival of ex-Gainsborough Trinity and Ilkeston Town attacker Reco Fyfe.
Manager Steve Chettle told the club’s website: “We’re delighted to welcome both Terry and Reco to Basford and both will go straight into the squad for this weekend's fixture against Stourbridge in the FA Cup.
“I worked with Terry during my time at Notts County with the first team and was a big part in the successful play-off season in League Two under Kevin Nolan.
“He also has massive Football League experience with Lincoln City and will bring a wealth of knowledge and skill to our group.
“Reco joins us after playing at Gainsborough during the last season and with the changes there, he was looking for a new challenge.
“He is a creative attacking striker and has an eye for a goal.”
Basford host Stourbridge in the FA Cup today.