In a presentation to supporters, owner Ann Budge said she hoped the structure would be open for September 2017.
The Edinburgh club also said they are confident it will be "completely paid for, with no bank debt at all."
They say funding plans will be revealed "shortly", with the formal design plans yet to be submitted.
The club will now enter into a period of public consultation.
Hearts add that they have been in discussions with supporters' group Foundation of Hearts, who are aware of how the project will be funded.
The new stand will bring the capacity of the stadium up to just under 21,000.
Hearts say they have raised 50% of funding for their proposed new main stand, with the cost of redeveloping Tynecastle estimated at £11-12m.