The firms said that 95% of Aberdeen and 99% of Standard Life shareholders had approved the deal, with Aberdeen describing it as "overwhelming support".
"The two businesses’ investment capabilities and distribution channels are highly complementary and by combining them we are well positioned to compete in an evolving global market environment," said Aberdeen chairman Simon Troughton.
Standard Life chairman, Gerry Grimstone, described the deal as "one of the most significant events" in the company's almost 200-year history.
He added: "Proudly headquartered in Scotland, and employing some of the best talent in our industry, our new combined company will continue to put our customers and clients across the world at the centre of everything we do."
The merger is still on track for completing by 14 August, Grimstone said.
Meanwhile, Standard Life is reportedly continuing its M&A rampage after beginning merger talks with rival provider Scottish Widows.
According to the Sunday Times, the two firms will begin negotiations this week.
Lloyds Banking Group-owned Scottish Widows is in the top five of UK life insurance providers by reserves, with £110bn of assets under management.
Aberdeen already has a tie-up with Lloyds after it acquired Scottish Widows Investment Partnership from the banking group in 2014 for £650m in shares. SWIP’s AUM accounts for about one third of Aberdeen’s.
Lloyds subsequently has an approximate 10% stake in Aberdeen.
A Standard Life spokesperson said the firm did not comment on market speculation.
However, a prospectus sent out to Standard Life shareholders in May alluded to further acquisitions from leveraging the relationship with Lloyds.
It said the combined group “will benefit from strategic relationships with a number of leading global organisations, including Lloyds Banking Group”.
It added, the combined group “looks forward to working with Lloyds to explore ways to build on Aberdeen’s existing partnership”.