The versatile midfielder, 18, is available for selection from Monday, when the Rocks go to Sussex rivals Horsham for an Isthmian premier division encounter.
Blake has been without skipper Calvin Davies, Harvey Whyte, Isaac Olaniyan, Kieran Douglas, Ben Anderson and Spencer Spurway as well as Dan Smith, who recently departed after sustaining a season-ending groin problem.
Osbourne joined the Cherries at under-10s level after playing for Ringwood Town. He can also play at full-back, and is said to be “a hard-working, intelligent and forward-thinking player”.
Blake said: “We obviously need reinforcements given our injury list so it is a great opportunity for Charlie to come in. He’s got some great qualities and will benefit from playing men’s football.”
Bognor host Enfield Town on Saturday and go to the Camping World Community Stadium on Bank Holiday Monday, looking to build on their second half display in the 2-2 draw against Wingate & Finchley on Tuesday.
Blake’s patched-up outfit trailed 2-0 at the break but a double from striker Dan Gifford in the second half gave the hosts a point.
Welcome to the Rocks, Charlie.