The 22-year-old, who made a big impression during a month's loan with the Pilgrims last season, is back with United until January initially after a fresh deal was agreed between the two clubs.
Wright will not be permitted to play against the Minstermen in October's league fixture but subject to final Football Association and National League ratification, he will be eligible to feature against Chester FC on the opening day of the season next weekend.
Wright won promotion from National League North with Harrogate Town in 2017-2018, alongside the likes of Jordan Thewlis and Dominic Knowles, and scored twice in four appearances on loan with the Pilgrims last season.
Reflecting on Wright's return to The Jakemans Stadium, United boss Craig Elliott told bufc.co.uk: "I am delighted to welcome Jake back. He is a player who did well for us during his brief loan spell here last season and I am now looking forward to working with him for an extended period.
"He is another exciting forward talent to add to the options we already have in place."