Veltman was offered a new deal by the Seagulls this summer but opted to move on as he departed the side as a free agent.
The 34-year-old played 165 Premier League matches and spent six seasons with Brighton where he showed qualities that the Hammers are keen to add to their promotion pushing side ahead of the new season.
Veltman had been training with Jong Ajax in recent weeks to keep sharp and has now put pen to paper with West Ham this week as he revealed how happy he is to join the now Championship side.
“I’m delighted to have signed, and I can’t wait to get started. The project here really excites me.
“I spoke to Nuno (Espírito Santo), as well as my family and my agent, and everything added up. We know that West Ham need to be in the Premier League, and for sure that is our goal for the season.
“I think I bring my experience, my winning mentality and togetherness. I bring leadership - I’ve been the captain at Ajax, and I enjoy talking to my teammates and using my experience to help the squad.
“I’m just so excited to give everything, to meet my new teammates and to see all the supporters too.”
Reports state Veltman also received offers from French side RC Strasbourg and Brazilian club Botafogo but it was West Ham who tempted him to stay in England and fight in the Championship.
Following the departures of Crysencio Summerville and Mateus Fernandes, West Ham boss Nuno Espírito Santo continues to rebuild a West Ham side who are tipped to shoot back up to the English top flight next season.