Bectu members voted 92% against the principle of selling the technology division to German firm Siemens while a second vote found 53.2% rejecting the current offer on terms and conditions, including pensions.
Union representative Luke Crawley said that despite the resounding votes against the sale, Bectu would await the BBC's response to a letter it sent over a week ago on issues such as child-care.
However, Crawley said he expected the response - expected later this week - to be 'more positive than negative' and that strike action was unlikely. He added that concerns over matters such as pensions had now largely been resolved.
The union previously arranged two rounds of strike action - one of which was due to affect coverage of the Olympic opening ceremony - but these were cancelled following new offers from Siemens.