Teenager Woodrow trained with the Shrimpers on Monday and it was enough to persuade manager Phil Brown to go ahead with a move for the 18-year-old.
The England youth international, who began his career at Luton, is under contract at Fulham until 2016 and was a key player for the Cottagers' Under-18 side as they were recently crowned national champions two years running.
"We're pleased to have Cauley here," Brown told the club's official website. "He's someone I've seen play and is maybe what we're missing in terms of striking options.
"He applied himself really well during training and I'm sure he'll do well during his time with Southend United. He's with us for a month to begin with before we assess the situation."
Woodrow added: "I'm delighted to be here and looking forward to getting some first-team football under my belt.
"I really enjoyed my first day with the players, they've all been great. I'm now just looking ahead to this weekend's game against Morecambe."