The 20-year-old, who has penned a three-and-a-half year deal at the Goldsands Stadium, made 24 appearances for Leyton Orient this season before his contract expired earlier this week.
"He is a young goalkeeper with a lot of potential to get better," Cherries boss Eddie Howe told the club's official website. "He is a good size and a good kicker of the ball - he has all the attributes to be a really top goalkeeper.
"He is certainly going to be a valuable addition for the future."
Allsop started his career at West Brom, gaining five caps for England Under-17s, before joining Millwall in 2011.
The stopper also played for Icelandic side M~rsttafilagip Hvttur before joining up with Leyton Orient in July.
"He's coming here to compete for the number one shirt - he's not coming here to make up the numbers. It's up to me to pick who I think is the best but he's going to have a lot of competition for places."
- Sports & Recreation