Wright`s future was hanging in the balance after parent club Bristol Rovers signalled their intention to sell him after his six-month loan deal at the Greenhous Meadow expired this week.
Manager Graham Turner had been uncertain whether Shrews would be able to hold onto his services with the club unable to agree terms with Rovers, but that has now been sorted.
The attacking midfielder will be keen to continue where he has left off for the Shropshire outfit over the first half of the season, netting 10 goals to lead their scoring chart.
Wright`s permanent deal has coincided with the signing of 20-year-old Collins from Premier League club Villa.
Collins has spent the last two months on loan at Burton, playing against Town on New Year`s Day, where he scored five goals in 12 games. He has penned an 18-month deal and could make his debut at home against Morecambe on Saturday.