His contract at the Premier League club was due to expire next year but the Blues drove a hard bargain for the forward, who will reportedly cost Madrid an initial €100 million ($113 million), with another €45 million in potential add-ons.
More in the "Real world" gets only the team captain Sergio Ramos - 12 million euros per year.
Zinedine Zidane was re-handed the reins in March, nevertheless, and now president Florentino Perez is going on a summer spending spree - with deals for Eden Hazard (£130m), Jovic (£50m) and Militao (£45m) already wrapped up.
"For Real Madrid, they are getting a phenomenal footballer and for Eden, there couldn't have been too many new chapters in his career", Martinez said.
Less clear is where Hazard will fit into Zidane's starting line-up.
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That indicates that the injury is not severe, so quite likely a "Grade I" hamstring injury at the most, which typically takes three weeks to return from.
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Faf du Plessis' men now have a single log point and find themselves holding down 9th place on the tournament table . As a result, both teams find themselves in a hard position, heading towards the latter half of the group stage.
Hazard contributed to 31 goals in the league last season, scoring 21 in all competitions for Chelsea - his best ever tally at the club.
Hazard had one year remaining on his Chelsea contract but said it was his dream to play for Real, and Belgium boss Martinez believes the forward will be a ideal fit for the Spanish giants.
Madrid want to sell Bale to raise money for more signings, with French left-back Ferland Mendy the next player expected to arrive, from Lyon.
Chelsea have reportedly identified Valencia's Goncalo Guedes as Eden Hazard's long-term replacement and have offered £62m for the Portuguese worldwide.
Hazard, 28, is moving to Spain after helping Chelsea win the Europa League and finish third in the Premier League.
Chelsea had just won the Champions League when Hazard chose them over several other clubs but they have failed to replicate the success in the competition.