As part of the deal VT Group will also inject 43 million pounds of capital into BVT, relating to the performance of certain export contracts, on completion of the deal.
VT will seek approval for the transaction from its shareholders at a general company meeting next month with BAE expecting the deal to be complete before the end of the year.
BVT, which owns the Govan and Scotstoun shipyards near Glasgow as well as two in Portsmouth, was set up as a partnership between BAE and VT Group in June 2008.
"This completes the final step of our exit from our shipbuilding and related activities. It will leave us in a strong financial position with net cash on our balance sheet and positions us to continue to pursue a growth strategy focusing exclusively on support services," VT Chief Executive Paul Lester said in a statement.