Right-back Birch, a 23-year-old who hails from Ellesmere, has been without a club since leaving AFC Fylde in the summer and joins until January.
He was a schoolboy at Everton before leaving for Burnley’s under-23s in 2015.
Boss Gavin Cowan is making changes to his struggling squad who have lost three games on the spin, including an FA Cup exit to lower-ranked Nantwich and a defeat at previously winless Blyth Spartans.
And another signing is expected before the weekend, where Telford are without a game due to their Cup exit.
Birch, who attended Lakelands School in north Shropshire as a youngster, has an impressive pedigree having represented England at under-16 and under-18 level.
He impressed with the National League Coasters last season, making 26 appearances as Fylde made two Wembley appearances in the play-off final and FA Trophy.
He played 90 minutes, before coming off as an added time sub, as his previous club beat Leyton Orient – who conquered Telford in the semi-final – 1-0 in the national stadium.
Left-back Steph Morley departed the Bucks earlier in the week. Morley rejoined National North rivals Leamington as Cowan revealed he only wants players interested in representing the club.