A site bordered by Bolley Avenue and Oakhanger Road will be redeveloped following approval by East Hampshire District Council.
Outline permission was given as part of a hybrid application that includes 2,400 homes, a new town centre, schools and space for businesses.
The development comprises one- and two-bedroom flats plus two, three, four and five-bedroom houses.
Cllr Nick Drew said: “When I looked at this originally I was very much concerned – we’re losing a wood, we’re losing a natural environment. Our own officer – who I know is incredibly good at looking after and defending our trees in East Hampshire – does not object.
“For me the reason why is because it allows East Hampshire District Council to protect the A and B category trees that are there. I saw a comment from one objector saying we don’t need housing. Well, we do need housing – there is a huge demand.”
Cllr Keith Budden added: “I don’t know whether it’s Christmas or what but I’m actually finding that I’ve got nothing to criticise in this application. I think it’s very good.
“I’m particularly pleased to see the houses are going to be heated by air and ground source heat pumps rather than gas boilers and I think that’s a very welcome move at the present time.
“I’m also pleased to see there’s early provision for bus routes.”