The 44-year-old has spent the past five years in charge of Tonga, leading them to a World Cup semi-final in 2017.
He had been working as assistant to ex-Saints boss Nathan Brown at NRL side Newcastle Knights and became interim head coach when Brown left in August.
Woolf has signed a two-year deal with Super League leaders Saints, with a further 12-month option.
"I'm confident we can achieve great things together," Woolf said. "I'm excited and privileged to be joining St Helens as head coach. It's a great opportunity for me."
Woolf's first role as head coach of a top-flight club has come as caretaker at the Knights.
He oversaw victory in his first game in the job, a 38-4 win over the NRL's bottom side Gold Coast, but they were thumped 54-10 by Penrith at the weekend.
Woolf will officially take charge on 1 November, replacing fellow Australian Holbook, who has picked up the League Leaders' Shield with Saints in each of the past two seasons.
The Gold Coast Titans-bound boss will be looking to finish as a double winner, with October's Grand Final at Old Trafford a major focus as they look to finish as many as 18 points clear of their nearest rivals at the top of the table at the end of the regular season.
Saints chairman Eamonn McManus said Woolf, who previously held a number of coaching jobs at North Queensland Cowboys, is "ideally qualified" to build on Saints' recent successes.
"He has the experience and expertise to bring the best out of our existing squad and to improve it further," McManus said.
"We are very confident that the Saints will seriously compete for honours under his tenure and that we will continue to play attractive and exciting rugby league."