The former Harrogate Town man played 26 times for Avenue last season in a variety of positions, but ended the season playing a number of games in the centre of defence.
Nowakowski, who initially joined the club on loan from Darlington in October, has also featured as a centre forward as well as in his preferred position of central midfield.
The 29-year-old returned to the North East briefly after a two-month loan spell, before making the move to his hometown club permanent just before Christmas.
Bradford-born Nowakowski was a part of the Darlington side that won the Northern Premier League in the 2015-16 campaign, before falling out of favour following the promotion.
Prior to joining the Quakers in 2015 the towering utility man had spent all of his senior career at Harrogate Town, where he made well over 100 appearances at National League North level.
He came through the ranks at Leeds United, where he progressed as a right winger before his height and strength saw him converted into an enforcer at Wetherby Road.
A box-to-box midfielder, Nowakowski is strong in the tackle and is capable of chipping in with the odd goal as well.