Gibbs was one of a host of Gunners players to enter the final year of their contracts at the Emirates this summer, leaving the club faced with the prospect of losing the defender on a free transfer in 2018.
Deciding to cash in on the England international, Arsenal initially demanded a fee of £12m for the 27-year-old left-back, a fee which saw some Premier League sides, including Newcastle United and Watford, drop their interest in the player.
West Brom also baulked at that initial valuation but struck a deal with the Gunners on the penultimate day of the summer transfer window, much to the delight of Pulis.
I just thought Gibbs was too expensive," Pulis said, the Express and Star report. "The £12m that Arsenal were talking about at the beginning of the season was too expensive.
"To get him for £5m over a period of time now is a good deal for us.
"We've got to get him fit. I think he has struggled with injuries over a period and that's been a big factor at times in his career.
"You look at him and he's a racehorse – he's quick and he's different to 'Grego' [Grzegorz Krychowiak], who's a lot stronger physically and 'Burkey' [Oliver Burke], who's a lot stronger physically."
Arsenal academy graduate Gibbs made only eight Premier League starts under Wenger in 2016-17 as he largely played second fiddle to Nacho Monreal and missed the FA Cup final victory over Chelsea due to illness. Gibbs featured 230 times in total for Arsenal, winning three FA Cups and two Community Shields.