Birch, 23, was brought in as a free transfer at the beginning of October during Gavin Cowan's squad re-shuffle having began the season without a club.
The former AFC Fylde man, an FA Trophy winner last season, initially joined Cowan's men until January.
He has since made 10 National League North appearances, starting nine, and put in some consistent displays on either side of defence.
Birch, who was born in Wrexham but grew up in Ellesmere, will remain a Telford player until the end of the season.
Cowan's men have picked up seven points from a possible nine over a busy six-day festive period.
Telford, now 13th, continue their aim to move up the National North table with a home clash against promotion contenders Brackley Town on Saturday.
Meanwhile, midfielder Jon Royle – Telford's longest-serving player – was due to finish his loan spell at Bradford Park Avenue yesterday (January 1). The 25-year-old played six times for the division's bottom club.