Rodrigues, who has for the past five years chaired Britain’s largest port, the Port of London, will oversee the agency, which serves as the UK’s shipping regulator – with oversight too for cruise.
The appointment was confirmed by transport secretary Grant Shapps on Tuesday (20 April).
The Department for Transport (DfT) said Rodrigues would bring "extensive international experience" to the role having held a wide range of roles across tourism and the arts, and in "public diplomacy".
"His leadership will contribute to the MCA’s ongoing plans to transform the agency as it works on innovation and regulation, while seeking to grow the UK flag and helping boost the maritime economy," said the DfT.
Shapps said Rodrigues’s appointment came at a "hugely important moment" for the UK as the country seeks to emerge from the Covid crisis.
"This appointment is part of a wider commitment to generate growth in the maritime sector, encourage greater investment in the UK and promote the UK flag as a world-class register that attracts quality shipowners," said Shapps.
The secretary of state also paid tribute to Michael Parker, the first MCA chair, for his work establishing its remit and directing the organisation over the past four years.
Rodrigues said he was looking forward to supporting the MCA and its team in adapting to "the changing needs and commercial requirements of international shipping".
"The UK is a world-leading maritime nation," he said. "Ensuring that the MCA provides an effective and responsive service is central to retaining this position."