Johnson, who managed the Welshman at Yeovil, told the club website: "He has trained with us for the last three weeks and we have seen what he can do.
"He can play on either wing and can play as a striker."
Davies' first spell with the Glovers saw him score 25 goals in 110 games and earned him a move to Nottingham Forest in 2007.
If I can get him back to his best we have an absolute bargain and I am sure we will see the best of him
Peterborough boss Gary Johnson
But since then he has struggled to overcome a variety of injuries and, after a loan spell at Brighton, spent the second half of last season on a short-term contract back at Huish Park.
"He had a bad injury that wasn't diagnosed for a while and that stopped him playing as many games as he should have done of late," Johnson added.
"However he is back fully fit and raring to go.
"If I can get him back to his best we have an absolute bargain and I am sure we will see the best of him."
The former Southampton trainee has one Welsh international cap to his name, coming on as a substitute in a 2-1 defeat against Trinidad & Tobago in May 2006.
Source: BBC Sport
Source: BBC Sport