It comes as the 12-strong restaurant chain reported a 5.7% rise in sales to £9.7m in the first seven months of the current financial year.
This is the first official role for McVeigh since he sold craft beer bar chain Draft House to BrewDog in 2018.
Breakfast Club, which launched on Soho’s D’Arblay Street in 2005, opened a café on nearby Berwick Street this autumn which it says is now outperforming its original location.
The group says it is planning further expansion in 2020 after negotiating a new bank facility with Santander earlier in the financial year.
It says its regional sites in Brighton and Oxford are performing well and there is a ‘particular focus on finding similar locations outside London’.
“As always, we are cautiously optimistic about the future of The Breakfast Club,” says Jonathan Arana-Morton, Breakfast Club founder and CEO.
“We have negotiated some fairly choppy waters and I am delighted with the resilience the team and this business has shown through a tough few years for the sector.”
Accounts for the year ending March 2019 will be filed shortly and show sales of £15.7m, an increase of 3.3% on the previous year. Group EBITDA for the year rose 39% to £744,000.
“I have been working closely with Jonathan Arana-Morton over the past six months and I'm immensely excited to join the board of what many regard as one of the strongest brands in the sector,” says McVeigh.
“The group's strong trading performance in and outside London suggests that further expansion is an option in the coming years.”
Breakfast Club launched a £750,000 crowdfunding campaign in late 2018 to fuel its next stage of growth, but failed to hit the target.