Woodman, 49, has 15 years coaching experience and will be in the dug-out for Good Friday’s National League game with Wealdstone.
He arrives with the Hayes Lane club in the middle of a promotion battle.
Bromley sit ninth - just a point outside the top seven - but have lost their last two matches to Sutton United and Wrexha,.
Woodman has previously coached at West Ham, Newcastle United and Charlton Athletic.
He says the time is right to move into a number one position and told the club’s official website that he cant’ wait to get going.
“I am delighted to be given the opportunity to lead such an ambitious club and am looking forward to working towards fulfilling that ambition,” he said.
“The chairman and his vision for the club, along with the existing and planned facilities make for an incredibly exciting time ahead for players, staff and supporters.”
He replaced Smith, who left last week after six years in charge.