Gibbs, 27, made his West Brom debut in Saturday’s 3-1 defeat at Brighton after signing for just £5m.
But boss Pulis says his patience paid off in his raid for the England left back.
“The £12m Arsenal were talking about at the beginning of the season was too expensive,” he said.
“To get him for £5m over a period of time now is a good deal for us.”
West Brom boss Pulis insists Gibbs must beef up to stop his injury problems though.
“We’ve got to get him fit,” he said. “He’s struggled with injuries over a period and that’s been a big factor at times in his career.
“He’s a racehorse – he’s quick but he’s different to ‘Grego’ (Grzegorz Krychowiak) and ‘Burkey’ (Oliver Burke), who are a lot stronger physically.
“So we’re going to have to make sure Gibbo knows what you have to do to maintain your fitness at this level.”
