
Heath, 33, played in the Premier League with Leicester City before signing for Leeds in 2006 – where he went on to make 52 appearances, scoring four goals.
Heath has also played for Brighton & Hove Albion and Colchester United, and was most recently playing under Miller at EvoStik Division One side Harrogate Railway.
Heath said: “When Billy offered me the chance to join him at Tadcaster Albion, I knew instantly that I wanted to join the club.
“Tadcaster have had a very exciting couple of seasons, and I’ve been very impressed with the ambition of everyone involved with the club.
“I’ve thoroughly enjoyed working with Billy over the last season, and I look forward to seeing what we can achieve together at Tadcaster.”
Leicester-born Heath was a key player in the Harrogate Railway side last season – winning Player’s Player of the Season.
Tadcaster Albion Chairman Matt Gore said: “Matt has played at every level from the Premier League to the EvoStik, so he brings with him a wealth of experience and great leadership.
“Billy obviously thinks very highly of Matt and was keen to make him his first signing, so we’re delighted that he’s joining us.”