The acquisition is expected to add around £2.3 billion to Liontrust's client assets, taking them to around £8 billion.
The sale followed the completion of a strategic review of Alliance Trust's business, which will shift the venerable Dundee-based trust to a more aggressive return target and focus on its popular savings platform.
The deal will be funded with £17 million in new Liontrust equity, £3 million in cash, and up to £10 million further when the deal completes.
Chief executive of Liontrust John Ions (pictured) said: 'The acquisition of Alliance Trust Investment puts us in a very strong position to meet this demand and we look forward to promoting the team and their funds in the UK and across continental Europe.'
Alliance Trust's sustainable investment team, led by Peter Michaels, will transfer with the business, alongside 11 ethical mandates.
'We have been very impressed by Peter Michaelis and the team at ATI,' added Ions.
'They will be an excellent addition to our seven teams as they are very experienced, have a clear and robust investment process and have shown that sustainable investment can provide strong investment returns as well as meeting investors' values.'
Former Alliance Trust chief executive Katherine Garrett Cox stood down at the beginning of the year, less than 12 months after losing a bruising battle with activist investors led by US fund Elliot International.
The fund installed three non-executives to the board who are likely to be keen to realise some value in the business, following several years of below-target returns from the Alliance Trust investment portfolio.
Following the review of operations, Alliance Trust's investment portfolio will move from a target return of MSCI World +1 to +2. Asset management will be decentralised to a number of teams, and the company will introduce a programme of share buybacks to support value.
Trust chair Lord Smith of Kelvin said: 'We believe there is good appetite for a global equity investment trust and that will remain our overall positioning. However, we are proposing a new approach to the investment management of the equity portfolio. Our proposal is that we will move from a single manager to multiple equity managers. All managers will be rated best-in-class and each will create a focused portfolio of their best investment selections.
'We are confident that this exciting and differentiated investment approach will help to improve Alliance Trust's performance on a consistent basis.'