The 6,500sq m superstore plan also include a £500,000 training centre, which will give youngsters the chance to learn skills including bicycle maintenance and arts and crafts.
Van hage's centre was hit by teething troubles when it opened in 2010. It now turns over £4.5m a year. Dobbies recently opened a rival garden centre in Peterborough.
GPI chairman Gordon Edington said: "At the moment we have Van Hage on one side of the site but nothing on the other. This second phase is key to the development of the area.
"There is a lack of supermarkets in the north of the city, and this problem will only grow when more houses are built.
"It will also bring 300 jobs, which will be suitable for lots of people.
"We are not in discussions with firms yet, but it is likely that it will be run by one of the big supermarkets.
A public consultation about the proposals will be held between November 14 and December 6, and a planning application is expected to be submitted to Peterborough City Council before Christmas. It is hoped the development will be open in the spring of 2013.