Odegaard, 22, had an outstanding loan spell with Real Sociedad last term before returning to Real Madrid, where he badly struggled for regular playing time in the first half of this season.
Zinedine Zidane was keen to keep hold of Odegaard but the midfielder, desperate to boost his minutes, pushed for a temporary move out of the Bernabeu and Arsenal struck a deal with Madrid towards the end of the January transfer window.
After being eased into the starting XI by Mikel Arteta, Odegaard has quickly become a key player for the Gunners and was brilliant on Sunday as the north London club came from 3-0 down to draw at West Ham.
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