Alabama National shareholders will have a choice of $80 per share in cash, shares in RBC, or a mix of both.
According to Reuters the offer price is a 50.6 percent premium to Alabama National's closing share price of $53.12 on Wednesday.
The deal follows moves by RBC to add to its US assets, having previously bought Raleigh in 2001 for $2.3 billion, and will improve the presence of RBC in the south-east of the US.
There was a notable 45 per cent hike in Alabama National shares on Thursday morning, leaving them at a price of $77.
Al Savastano, an analyst at Fox-Pitt Kelton in New York, told the news agency, "If you're going to pick up anywhere in the US to grow, it would the south-east, because it's showing the most growth in terms of population."
The deal is expected to close in early 2008.