Brewin will pay around €44m (£38m, $49.4m), including €37.15m on completion plus an additional fee of around €7m.
The transaction is subject to regulatory approvals and completion is expected to take place in the second half of 2019.
It was widely reported in April that Brewin pipped Rathbones to the post and had entered exclusive talks with Investec about the deal.
Brewin said it builds on its existing business in Ireland; which will, post-completion, have assets under management in excess of €4.6bn.
Some 31-investment staff, 19 support staff and around 5,000 clients from the Dublin-headquartered Investec business will transfer to Brewin.
Growing in Ireland
David Nicol, chief executive of the Brewin Dolphin group, said: “This acquisition, which is consistent with our strategy of growth in assets under management, provides us with an exciting opportunity to strengthen, substantially, our existing presence in the Republic of Ireland, one of Europe’s fastest growing economies.
“We will also be in a stronger position to benefit from the country’s growing demand for discretionary and advice-led services, supported by favourable demographics, with the country having the youngest population in Europe.
“Our businesses are highly compatible in terms of culture, values, investment philosophy and client-centric approach, which combined with our established platform, will enable us to meet more effectively the growing demand for wealth management services in both the UK and the Republic of Ireland.”
Brewin has a £70m ($91m, €81.1m) war chest that it has deployed to push forward its inorganic growth plans.
The money has been spent on various M&A deals in recent years, as well as some strategic initiatives over the last 12 months.
The company did not disclose how much money it had left to pursue further initiatives, but Brewin did reveal in its latest financial update that it plans to raise gross proceeds of around £60m through a share placement scheme.
The deal was announced alongside Brewin Dolphin’s financial results for the half year, ending 31 March 2019.
It reported a decrease in profit before tax of 12.9% compared to last year, as it came in at £29.7m from £34.1m in March 2018.
However, total funds under management for the group rose to £42.4bn, from £39.7bn in H1 2018.