The 22-year-old has penned a four-and-a-half year deal with the Hammers, with the transfer fee reported to be around £3.7million.
"I'm unbelievably proud and happy to join a club as big as this," Byram told the club's official website.
"I'm just looking forward to what the future holds and hopefully I can achieve things with the team going forward."
Full-back Byram was born in Essex, but moved to Yorkshire as a child before joining up with Leeds aged 11.
Byram, who can also play in a more advanced role on the right wing, came through the youth ranks at Elland Road to make his debut in the 2012/2013 campaign.
He now has his sights set firmly on making an impact with the Irons.
"It's a childhood dream of mine to play in the Premier League, so to have the chance to get into a team like this and I just want to get my head down, work hard and hopefully get a chance," Byram added.
"I spoke to the manager and he is one of the main reasons which attracted me to West Ham
I think he's done unbelievably well with his team so far, so I'm really looking forward to working with him and his staff.
"My uncle and my cousin are big West Ham fans. It's nice to have them down here and they'll help me settle.
"I'm also really looking forward to seeing the new (Olympic) stadium in person. That was another big part in me wanting to come here. It's a massive part of the future of the club and I can't wait to see and hopefully play in it."
Source: PA