The National League Stones have been allocated an 18-acre location in west London by Hillingdon Borough Council.
Their current 4,000-capacity ground at Grosvenor Vale is restricting progress and the new plot of land is just over two miles from their current home.
The Freezeland Way site is adjacent to Hillingdon Underground Station and the club hope that can boost attendances.
Part-time Wealdstone sit 17th in the league and have never played EFL football before.
Wealdstone chairman Rory Fitzgerald said: “London Borough of Hillingdon's decision to allocate the club this land follows a long period of discussion and negotiation and will play an important role in safeguarding the future of the club and supporting its growth.
“On behalf of the Board, I would like to personally thank London Borough of Hillingdon for their support and we look forward to working closely with them as we take the project forward, subject to planning.
“The new stadium is fantastic news not only for our fans and players but the whole local community. As we progress, we will ensure that we optimise the benefits for local residents while also working to minimise and mitigate any potential environmental impacts associated with a construction project of this size.
“In addition, we are confident that the security and growth potential offered by the new stadium will help us attract the investment we need to realise our ambition of one day playing in the EFL.”