Expanding the World Cup to 48 teams is a "positive" step, according to SFA chief executive .
An initial stage of 16 groups of three teams will precede a knockout stage for the remaining 32 when the change is made for the 2026 tournament.
"We believe this is a positive step, particularly for the smaller nations," said Regan.
"Wales, Iceland and Northern Ireland at Euro 2016 showed the impact smaller nations can make," he added.
Fifa, the sport's world governing body, voted unanimously in favour of the change at a meeting in Zurich on Tuesday.
The number of tournament matches will rise to 80, from 64, but the eventual winners will still play only seven games.Why expand?
Fifa president Gianni Infantino has been behind the move, saying the World Cup has to be "more inclusive".
According to Fifa's own research, revenue is predicted to increase to £5.29bn for a 48-team tournament, giving a potential profit rise of £521m.