The 97 jobs will be created over the next five years.
The firm began operating in Northern Ireland in 2012 and now employs about 100 people.
Invest NI is supporting the investment with a grant of £727,500.
Axiom is based in the US and employs around 1,200 people.
The new posts in Belfast will have average salaries of £40,000.
They include a mix of lawyers, project managers and technologists.
Axiom provides out-sourced legal services.
It recently announced a major partnership with an investment bank to provide improved risk management in derivatives.
Kate Docherty of Axiom said the company had been "delighted by the success of our operation in Belfast and its contribution to our growth globally".
"Our expansion in this region is a testament not only to that growth, but to the skilled pool of available talent in Belfast who have made that success possible," she added.
The legal services firm Axiom UK is to double its Belfast workforce in a £9m investment.