Sky Sports understands the former Aldershot midfielder has agreed terms with Neal Ardley's men, after impressing in recent weeks.
Cooksley is now in contention to be involved against Burton Albion at the weekend.
Will Antwi is another who is back in contention to feature against Burton, as he looks to have overcome his recent injury problems which have limited him to just three games this year.
"Will's doing cardiovascular work and hopefully he can join in with the rest of the squad by the end of the week," said Ardley told the Hounslow Chronicle.
"I haven't really had him available for most of 2013. He did well in pre-season then had another setback, but hopefully he'll be back soon."
One man who will not be involved this weekend is striker Charlie Strutton - who is set to be sent out on loan.
"We might look to do something with Charlie to help his development," Ardley added.
"He probably won't get much playing time at the moment apart from bit-parts.
"For his sake I want to give him a month somewhere so he can get a run of games, stay fit and score some goals then come back to us full of beans."