The Rovers forward, who joined the club from Manchester United at the turn of the year, will first be involved with the senior squad in a World Cup qualifier before joining up with the Under-21s in the UEFA Championships that take place in Israel.
Norway's seniors have a World Cup qualifier against Albania in Tirana on Friday 7th June before King will jet to Turkey to link up with the Under-21 squad.
By then the Under-21s will have already faced hosts Israel on June 5, the next game on June 8 sees Norway take on Jason Lowe's England in Petah Tikva.
Norway end their qualifying group against Italy in Tel Aviv on Wednesday 12th June.
The winners and runners up from the two groups go through to the semi-finals on June 15 with the final taking place on Tuesday 18th June in Jerusalem.