Majority owned by Mexican Carlos Slim, FCC will begin work immediately and avoid disrupting games, with the project due to be completed by August 2022, the club said in a statement.
The contract is worth around 475 million euros (£408.67 million), Spanish newspaper Cinco Dias reported.
Last month Real Madrid announced it had secured a 575 million euro loan to finance its plans for a “digital stadium of the future.”
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(Reporting by Sam Edwards; Editing by Elaine Hardcastle)
