Experienced former Norwich City and Northern Ireland manager Nigel Worthington stepped down from the York job on Monday after weekend defeat at the hands of left them at Newport County left them one place above the relegation zone.
"In recent weeks, performances have not been up to my high standards and I take full responsibility for this," said Worthington, whose side drew 1-1 with Northampton in mid-August.
Tranmere currently prop up the Football League and that has spelled the end for rookie boss Rob Edwards.
The 41-year-old was handed his chance in the summer having previously been part of the backroom team at Exeter City.
The Cobblers travel to Prenton Park on Sunday 28 December.