The vote follows regulatory approval for the deal from the Financial Conduct Authority and the Central Bank of Ireland.
The new firm will be known as Tilney Smith & Williamson and will be the fourth largest UK wealth manager.
Chris Woodhouse, CEO of Tilney, said today: “We are delighted that Smith & Williamson shareholders have overwhelmingly voted in favour of the merger and can confirm that all regulatory approvals have now been received.
"This is a significant transaction and getting to this stage in the midst of a global pandemic is a real achievement. We now look forward to completing the deal over the coming weeks and bringing these two great businesses together.”
The progress comes after the deal became stalled earlier in the year when the Coronavirus pandemic struck.
However in June private equity firm Warburg Pincus stepped in to co-invest in the combined business alongside funds from Permira.
Warburg Pincus has invested £12bn in 120 financial services businesses including six wealth management firms.
The merged business will look after about £45bn in assets under management and generate about £530m in annual revenue.
Tilney, which looks after £25bn in assets and has 1,000 staff in 30 offices, has been expanding its Financial Planning arm in recent years with numerous hires. Smith & Williamson also has a growing Financial Planning arm.
The merged firm will be responsible for £45bn of client assets, of which 80% will be discretionary mandates or funds. It will have approximately 280 investment managers, 260 Financial Planners and a professional services business with 150 partners and directors.