Adrian completed his move from Real Betis yesterday.
"I am very fortunate to be able to work with such an experienced goalkeeper with such a long track record in the Premier League as Jussi Jaaskelainen," he said.
"I'm really looking forward to working with him on a daily basis and being able to receive tips from him which I'm certain will make me an even better goalkeeper.
"It's going to be an honour to be under the wing of such an experienced manager and that can only serve to make me a much better player.
"There is a very competitive squad at West Ham and, in my opinion, competition is what makes the group stronger and helps the club to go further in the competition."