The prolific 20-year-old scored 44 goals in 90 appearances during two seasons in Belgium and arrives at St James' Park for a figure reported to be in the region of 18 million euros.
Newcastle's official website (www.nufc.co.uk) said the fee for Mitrovic was the fourth highest in club history.
The player told VRT News & Sport that he hoped to equal the performance of Newcastle’s legendary striker Alan Shearer.
"I have played in a lot of impressive stadiums in my career but St James' Park is so big, I can't wait to play my first game here," he told the site. I know how passionate the fans are. This is a club with a very big history and the fans are a big part of that. There will be pressure here, for sure, but I like pressure."
Mitrovic, who scored a dramatic late equaliser in a 3-3 Champions League draw against Arsenal last season, has represented Serbia 14 times, scoring once.
The forward broke into Partizan Belgrade's first team as a 17-year old, scoring 15 goals in 36 games in his only full season with the Serbian champions in 2012-13.
Impressive performances for the under-19 national team that won the 2013 European Championship earned him a move to Anderlecht, where he continued to flourish.
He helped the Brussels club win the league title in his first season and was particularly impressive last term, scoring 20 league goals in 37 appearances as they finished third. The Serbian was Belgium’s top scorer last season and was arguably responsible for most of Anderlecht’s attacking prowess.
Mitrovic's physical strength, aerial power and clinical finishing should ensure that he copes well with the demands of the Premier League.
He becomes new manager Steve McClaren's second signing, following the acquisition of Netherlands playmaker Georgino Wijnaldum from PSV Eindhoven earlier this month.
"This is a fantastic signing for us," former England manager McClaren said. "We have fought off a lot of competition to secure a top young talent in Europe. It is another demonstration that we are wanting to push on."