In its third quarter update, the firm said assets under management rose 18.5% from 30 June to stand at £47.3 billion at the end of September.
The Speirs & Jeffrey deal, which completed in August, contributed to £6.7 billion of the increase.
Rathbones chief executive Philip Howell (pictured) said in a statement: 'This increase in scale places us in a strong position to continue to improve our service to clients and, mindful of recent volatility in investment markets, to maintain our disciplined investment in the business.'
Excluding the impact of this, assets under management rose by 1.8% over the period.
This compared to a decrease of 1.7% in the FTSE 100 index and an increase of 1% in the MSCI WMA Private Investor Balanced index over the three months.
The update also showed underlying net operating income rose 13.9% in the third quarter to £80.3 million. Within this, its investment management arm saw income rise 13.3% year on year to £70.8 million.
Funds under management in its unit trust business hit £6 billion, an increase of 3.4% from June 2018. However, net inflows dipped from £342 million during the corresponding period of 2017, to £121 million. The firm said this reflected 'a more difficult trading environment for asset management generally'.
Net operating income in the funds unit was 18.8% higher at £9.5 million.