The 30-year-old, who was last with Marine AFC in the Evo-Stik Northern Premier League Premier Division, becomes the first new signing for Avenue boss Alex Meechan.
Sharp, son of former Everton and Scotland striker Graeme also featured for Salford City and Colwyn Bay last season, before joining the Mariners.
He started his career in Wales with Rhyl, before moving on to Bangor City where he scored 33 goals in forty games.
That form secured him a move to The New Saints, where he scored 22 goals in twenty-nine appearances, winning the Welsh league title and appearing in the Champions League.
He moved on to Telford, where he in fact played in attack alongside Alex Meechan, scoring 15 goals in the team’s first season back in the Conference.
Spells at Lincoln, Hereford United and Stockport County followed before he joined Colwyn Bay last summer.