Eriksson, 64, was presented by his new employers at a press conference at the club's Al-Maktoum Stadium on Monday evening.
The move comes just days after the Swede turned down a job on the coaching staff at German second division side 1860 Munich.
Al-Nasr will be Eriksson's 16th coaching job and follows recent spells in charge of the Ivory Coast national team and Thai club side Tero Sasana.
However, Eriksson denied the move was driven by money, insisting his reasons for taking the job were purely footballing ones.
"I can promise you the jobs in Ivory Coast, Thailand and here were not for money - absolutely not," he said.
"I don't complain about the salary - I'm happy about that - but it's not for money. It's for the love of football and to see new parts of the world."
Al Nasr, who are coached by former Italy goalkeeper Walter Zenga, currently lie fifth in the UAE Pro League.