Langmead netted at the weekend to persuade Town to offer him a two-and-a-half year deal.
Peters told ShrewsWeb: "I'm very, very pleased with the deal and it's a great move for the club."
Peters also said that part of the reason for the reason for the signing was to free up another loan slot, and to remove the possibility of Langmead being recalled by Preston.
He also confirmed that a 'small fee' had changed hands for the deal.
The news comes on the same day that Town dismissed an offer from Chester for Jamie Tolley.
The offer, of £5,000 rising to £10,000 on appearances was dismissed by the Town board.