The striker joined West Brom on a two-year deal to return to the Barclays Premier League for the first time since 2008.
In his first spell he scored just 12 goals in 65 games for City after a £6million move from Heerenveen in 2006, before being offloaded to Celtic two years later.
The 29-year-old helped the Hoops win four Scottish Premier League titles but was released in the summer and has moved to The Hawthorns.
Samaras will not feature in the Baggies' trip to Southampton today but wants to show how much he has developed.
"I'm more mature now and know football better than when I was younger," he said.
"I had seven beautiful seasons at Celtic and I'll keep all those good things.
"Now it's a new start and challenge in my career, and I'm looking forward to that. As a professional footballer you want to get better and better, and I believe I have changed from 22 to now, like anybody would in any job."
Southampton and Malaga were interested in the Greek international, who helped his country reach the last 16 of the World Cup in the summer, but Samaras chose Albion.
"It was an easy decision for me to come here," he said.
"I had a really nice chat with the gaffer: he's Scottish so we spoke our language.
"In the end I believe this is a new challenge in my career and I'm ready to take it."