Tristan put pen to paper with Scott Duxbury after the Hammers' chief executive had flown to Rome to finalise negotiations with his representatives.
West Ham boss Gianfranco Zola moved for the player following a two-week trial, with England international striker Dean Ashton sidelined following ankle surgery.
Tristan told his club's official website: "I am really happy to be at West Ham. They are a big club and London is a great city.
"I want to show the fans that I can score goals and help the team to go up the league. I am excited to be here."
On Zola, the player continued: "The manager has spent lots of time working with me. He has helped me a lot and I want to say thanks to him by scoring lots of goals and doing well for the club.
"I am very grateful to the manager for giving me the opportunity to play here.
"I have been really impressed from the moment I arrived at the training ground.
"The coaching staff and the players have all helped me to settle in. I had a lot of offers to go to other countries and play for a lot of money but I feel that I still have lots to offer and I want to show West Ham fans that I can still play at the highest level. That is why I am here."
The 6ft 1in forward, who is in contention to make his debut in Sunday's Barclays Premier League match at Hull, added: "I have always been impressed by English football whenever I have played here.
"The stadiums and the fans are great and it was always a dream of mine to come here and play.
"Now my dream is going to become reality. I am at a great club and I want to see if I can help West Ham get into Europe and play at that level.
"English football is very similar to Spanish in that it is very quick and technical.
"There is more of an emphasis on attacking football so I will have more chances to score goals.
"In Italy, it was more defensive, and not easy for forwards to get scoring opportunities. West Ham play the right way and that should help me to do well."
Duxbury added: "I am delighted that we have been able to secure the services of Diego, who is an experienced striker and has already had a positive impact.
"Diego will provide extra competition in attack and the manager has been impressed with his attitude and ability in training."