The 20000 seater stadium, which will be shared between the Swans and Swansea RFC, will be built over the coming year and is on course to open in September next year.
"I'm obviously pleased at the news of this agreement," Council leader Lawrence Bailey told the South Wales Evening Post.
"It represents a very important milestone in this scheme and gives the green light for investment.
"I don't think that people have fully appreciated the incredible complexity of this project which involves land deals, finacial packages, planning consents and reams of legal papers before a single piece of earth can be dug."