Unite members were set to stage three walkouts later this month in a dispute over the closure of a final-salary pension scheme.
The union said it was not recommending the deal to workers at the Oxford, Goodwood near Chichester, Hams Hall and Swindon plants.
BMW said it believed the offer was "fair".
Staff at the sites have already held four strikes - the first ever by BMW employees in Britain.
The union's national officer for BMW, Fred Hanna, said it was not recommending the new offer "as it will have different outcomes for different people and their pensions".
He added: "Members should be proud that by standing together they have forced BMW into making this offer.
"Without the action that Unite members have taken and the resolve they have shown in recent weeks, BMW would not have made this latest offer."
According to BMW, 67% of those affected by the changes who were eligible to vote backed the action.
A company spokesman said: "The company is keeping all staff fully informed and we await further feedback from Unite following its ballot.
"We believe the offer to be fair and in the long-term interests of both the company and all our employees."
The ballot is expected to run from 24 May to 9 June.
Planned strikes at BMW car plants have been suspended while members consider a deal.