The powerful writers' union's board of directors "voted unanimously to recommend the agreement," it said in a statement, adding "the strike ends at 12:01 am" Los Angeles time on Wednesday.
Turner, who was served with divorce papers this month after four years of marriage to Jonas, said in her petition that the couple had planned to raise their daughters in her native England.
Swift took home nine of the 11 awards that she was up for, including Artist of the Year, in a category made up entirely of women nominees for the first time in VMA history. Her Karma (remix) collaborator, Ice Spice, won the best new artiste award.