Ramos, 29, will sign his new deal together with Real president Florentino Perez at the Bernabeu stadium later on Monday, the club said on their website (www.realmadrid.com).
Local media reported the team captain, a dressing-room heavyweight and a huge fan favourite, would earn 10 million euros ($11.1 million) a season after tax, making him one of the best-paid members of Real's expensively assembled squad.
Ramos was strongly linked with a move to United following the end of last season, with reports in Spain and England suggesting he might be included in a swap deal for the English side's unsettled Spain goalkeeper David De Gea.
As well as tying Ramos into a new contract, Real are also reportedly poised to sign Croatia midfielder Mateo Kovacic from Inter Milan for a fee of around 30 million euros ($33.31 million).
Inter coach Roberto Mancini appeared to confirm Kovacic was leaving after Sunday's 0-0 friendly draw at home to AEK Athens, in which the 21-year-old did not feature.
"None of us are pleased, from the president, to me to the directors and his team mates," Mancini told reporters when asked about the player.
Kovacic is seen as ideal backup in the centre of Real's midfield for his Croatia team mate Luka Modric and Germany midfielder Toni Kroos and would compete for a place in the side with the likes of Isco, Asier Illarramendi and Casemiro.
(Reporting by Iain Rogers, editing by Sudipto Ganguly)
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