England fullback Gibbs left Arsenal for the Hawthorns on the penultimate day of the transfer window.
He returns to the Emirates Stadium on Monday evening (Tuesday morning AEST) as Tony Pulis's side take on the Gunners in the Premier League.
Gibbs came through the ranks at Arsenal before breaking into the first team at 18 and going on to represent the club 230 times in all competitions.
He was limited to just 11 Premier League outings last season and the northern summer arrival of Sead Kolasinac was always likely to force the 27-year-old out of the club.
A move to Watford failed to materialise before West Brom stepped in on the eve of deadline day, with Wenger gutted to see Gibbs move on.
Asked if letting Gibbs leave felt like losing a family member, he said: "Of course. And I believe that for (players that leave) it must be difficult to make that step as well.
"He did not ask to leave, it was a mutual decision. He wanted to play - he's 27, or 28. You want to play at that age.
"It was a difficult decision but on the other hand when a guy has given you so many years you have to accept that if he is not sure to play.
"It is a fact that we have got Kolasinac, you cannot keep three left-backs (along with Nacho Monreal)."
Wenger also admitted it was painful to lose players like Gibbs and Alex Oxlade-Chamberlain, who was sold to Liverpool on deadline day, after years of building their careers at the club.
"Ideally you want stability and you want players who carry the values for the generations," he said.
"Overall it's true that with Gibbs (it hurt) more than Chamberlain because he had been educated at Arsenal from the age of 10.
"When he arrived he was a left-winger. I transformed him into a fullback because he was not necessarily rated as a guy who would make it as a left-winger but I saw something in him that was very intelligent, with pace, that made me feel he could make it as a left-back.
"(Academy players) carry the values that you think are important, which are based on mental qualities, humility, respect and commitment, and as well football qualities which means you always try to play in a positive way. Plus real team play and focusing on a collective way."