It follows an agreement reached last month for the Government to take over the yard after the firm entered administration in August.
Administrators concluded three indicative offers for the business received from commercial parties were either not capable of being executed or did not represent a better outcome for creditors than the sale of the business to the Scottish Government.
A meeting of the board of directors of Macrocom - the company wholly owned by Scottish ministers that will own the Ferguson Marine business and assets - was held on Friday to consider and sign the contract.
Full completion of the contract and the final transaction is expected to take place in the coming weeks.
Finance Secretary Derek Mackay said the action taken would help to ensure a future for the yard.
"Our focus has always been on ensuring completion of the two public sector ferries at the best value for money for the taxpayer, while also working towards the delivery of the other vessels under construction at the yard, and in doing so, securing jobs for the workforce," he said.
"Today marks another important milestone in the transition into public ownership and I will also receive the Programme Review Board's report on the schedule and cost for delivery of the two ferries shortly.
"While we've been working with the administrators to bring the yard into public ownership, work on the ferries has been progressing and additional staff have been recruited.
"The action that we have taken will ensure there is a future for Ferguson Marine."