Egbuchulam who finished as the top scorer of the Nigeria Professional Football League (NPFL) last season was initially meant to join Tunisian side, .
The move however failed due to the unofficial approach of Etoile Sportive Du Sahel.
He signed a loan deal until the end of the season with an option of a three-year permanent move to the 2016 Swedish Cup champions
"Moving to Europe is a big dream come true for me," Egbuchulam told BBC Sport.
"I thank God for the opportunity and BK Hacken for the platform to play in European football."
Rangers have released a statement confirming the move and also wishing their former striker good luck at his new club.
“Wishing Chisom Egbuchulam all the best after he moved to Sweden. Thanks for the memories,” the club said on Twitter.
Egbuchulam has already been called up to the Super Eagles squad for their 2-1 away win at Zambia for the 2018FIFA World Cup qualifiers in October 2016.