Elvan served as transportation, maritime and infrastructure minister between 2013 and 2015 and development minister between 2016 and 2018, Anadolu Agency reported.
Turkish president Recep Tayyip Erdogan accepted Albayrak's resignation on Monday, the news agency said.
Albayrak, who is also Erdogan’s son-in-law, announced his resignation because of health reasons on November 8, news portal Duvar reported on Sunday.