Toft will report directly to Diego Aponte, MSC group's president, and Gianluigi Aponte, the company's founder and group chairman, the MSC spokesman said, adding that a start date has yet to be set.
Newspapers and trade publications have speculated that Gianluigi Aponte may be retiring as chairman of MSC, which is privately held, but the spokesman said on Monday that "reports that Gianluigi Aponte is stepping down are erroneous".
The spokesman added that both Gianluigi and Diego Aponte would "retain a close, hands-on role at the top of the business".
Maersk, the world's biggest container line, said last week that Toft, who had served as its head of operations, was leaving to pursue outside opportunities.
"MSC is confident that this appointment will bring significant value to its cargo businesses, building on the company's existing strengths and boosting its development plans even further," MSC said in a statement.
MSC, which also has a cruise line business, is the world's second-largest container shipping line and is seen by industry analysts as a challenger to Maersk's position.
Maersk is estimated to have a global market share of 17.8% or 4.19 million TEUs (20-foot equivalent units), with MSC at 15.9% or 3.74 million TEUs, data from consultancy Alphaliner showed.
(Editing by Alexander Smith and James Drummond)
By Jonathan Saul