New deals for the management duo have been in the pipeline for several months but they finally put pen to paper on Tuesday afternoon to tie them to the Robins until 2014.
Yates, who was appointed manager in December 2009, confirmed the deals had been agreed for some time but that he waited until a League Two play-off position was secured before signing.
"I'm very happy but I'm glad it's sorted because we have had it agreed for a while now," Yates told the club's official website.
"It has been on the backburner a little because we wanted to concentrate on the football, but we've achieved what we set out to achieve and now I think it was the right time to get it done.
"Both Neil and I are delighted to have signed a new deal which will see us here for another two years."