Brown arrives from Arsenal in an emotional transfer. Luis is the son of former Hammers fullback Kenny Brown and the grandson of Irons great Kenny Snr.
Robson told the club's website: "It’s a fantastic day for Luis, and for the whole Brown family. It’s great that tradition is continuing, and I’m sure he’ll work as hard as possible to try to emulate Kenny and Ken Sr.
“Luis can play in a couple of positions in defence, which is always useful. We’re all looking to maintain the high standards that have been set here over the last few years, and signings like this are a good step towards making that happen.
“All the boys are working to ultimately try and move themselves towards first team football, and we’re going to try and help them do that. It’s a really exciting season coming up, and we all can’t wait to get back on the pitch.”