United made the announcement on their verified Twitter handle on Wednesday.
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“Manchester United is delighted to announce it has reached agreement with Sporting Clube de Portugal for the transfer of Bruno Fernandes.
“The deal is subject to a medical and the agreement of personal terms.
“A further announcement will be made in due course.”
United will pay an initial fee of around 55m euros (£47m) though add-ons could increase the overall cost to 80m euros (£67.6m).
The two clubs have been negotiating throughout the transfer window with a breakthrough made on Tuesday amid reports of interest from Barcelona.
United, linked with Fernandes last summer, initially refused to meet Sporting’s demand for 80m euros upfront.
For the Portuguese club to receive the full amount, a series of conditions must be met – including United’s qualification for the Champions League.
Fernandes, 25, joined Sporting from Sampdoria for £7.2m in 2017 and has gone on to score 64 goals in 137 matches in all competitions, winning the Portuguese Cup with Sporting in 2018-19.
He has played 19 times for Portugal and was a member of the squad that won the UEFA Nations League.
He will follow in the footsteps of Portuguese stars Cristiano Ronaldo and Nani who joined United from Sporting Lisbon.
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