He told BBC Radio Cambridgeshire: "Obviously it didn't work out at Forest and I'm more than happy to come back here and start the new season here.
"I'm here until I hear differently from the chairman, I'm here for the season."
Boyd joined Forest in March but failed to secure a permanent move, making just six appearances.
Sounds like he is willing to stay put, think our beloved director of football needs to get that juicy contract drawn up
fozzyposh
It was expected the former Stevenage man would attract the interest of other Championship outfits, but Posh boss Gary Johnson has yet to receive any offers.
Boyd added: "You want to play as high as you can. I did quite well last year in the Championship and that's where I'd prefer to be playing.
"But there's no reason why we can't get promoted straight back.
"We've made some great signings and with the players we've already got we've got a strong chance of going up."
Johnson, who was appointed Peterborough manager while Boyd was at Forest, has had a busy summer already, bringing in defenders Kelvin Langmead and Mark Little, striker Dave Hibbert and midfielder James Wesolowski.
Norwich, Leeds and Millwall went up, so that's three big teams gone. Southampton will be strong but there's no-one to fear I think
George Boyd on League One
"I haven't had chance to speak to the boss, I'm sure I will in the next couple of days," said Boyd.
"He seems really good. His record speaks for itself, so I'm sure it will be a good season."
It was only 12 months ago that the Scotland B international was celebrating back-to-back promotions with Posh, and he sees no reason why his side will not be one of the favourites for League One success again this time around.
"Norwich, Leeds and Millwall went up, so that's three big teams gone. Southampton will be strong but there's no-one to fear I think," he said.
"You look at the league and most of the teams there were there when we were last in it."
Source: BBC Sport
Source: BBC Sport