The 22-year-old, who arrived in the autumn following a brief spell with Altrincham, has pledged his long-term future to the Pilgrims following a hugely successful second half to the 2024-2025 campaign.
Teale scored three goals in 26 appearances as the Pilgrims overturned a sizeable points deficit to earn a second season in the National League.
He began his career at Fleetwood Town and enjoyed a number of loan spells away from Highbury, including one north of the border with Arbroath.
Teale will report for pre-season training at the beginning of July as United return to fully professional status for the first time since 2007.