The founder and chairman of investment company Western Gulf Advisory, Syed failed in an attempt to buy English Premier League club Blackburn Rovers last year.
Syed's office said in a statement the deal to buy the La Liga club had been approved by the regional government of Cantabria and Spain's national sports council (CSD).
"I look forward to an active and long-term commitment to this great club and will invest all my knowledge and financial strength to elevate the club to the highest level of success in Spain and Europe," Syed said in the statement.
Racing representatives were not immediately available for comment.
Syed's foray into Spain follows the purchase of Racing's La Liga rivals Malaga by a member of the Qatari royal family at the end of last season.
A Mexican businessman is also trying to buy Real Oviedo, a former first-division club that has dropped to the third tier, Spanish media have reported.
A heavily indebted club in the north of the country, Racing have a famous fan in Spanish golfer and local resident Seve Ballesteros and have come under foreign control before.
Ukrainian-born American businessman Dmitry Piterman bought into the club and was president between 2003 and 2004.
The colourful Piterman hit the headlines when he clashed with the football federation (RFEF) over his attempts at coaching the team himself despite not having the correct permit.
Racing has suffered the financial problems affecting many of their Spanish peers. A study by a University of Barcelona accounting professor published last year showed it had total debts of almost 140 million euros.
They are currently 14th in La Liga at the halfway stage of the season, four points above the relegation places.
