French legend Zinedine Zidane's presence as reserve-team coach played an important part in the teenager's decision, he said.
The 16-year-old would not comment on his salary but media reports have put his weekly salary at about €45,000 per week ($51,000).
"It (money) has not been an issue at all for me. It was not an issue in my discussions with various clubs," the young attacking midfielder told reporters in Drammen, in southeast Norway, where he bid farewell to his former club Stromsgodset.
"I chose what was best for me in sporting terms," he added.
Ødegaard will fly this week to Madrid where he will train with the first team and play with the reserves, Real Madrid Castilla.
The Norwegian international — coveted in the transfer window by top clubs such as Bayern Munich, Arsenal, Liverpool and Ajax Amsterdam — stressed that third-division Castilla was trained by Zidane who he considered to be "one of the world's best footballers of all time".
On Friday, a day after his signing was announced, Real coach Carlo Ancelotti predicted a "great future" for Odegaard but urged that "patience" will be necessary as the Norwegian prepares to enter the club's first team.
"It's difficult to think that Ødegaard could play (in the first team) straight away," Ancelotti said.
"He's very young, we have to be patient with him. We're all convinced he'll play and will be an important player for Real Madrid," he added.