The film, written by JK Rowling and starring Eddie Redmayne as Newt Scamander, took a total of £15.3m.
It is the third highest opening weekend from the JK Rowling series, behind the two final Harry Potter films.
Warner Bros executive Josh Berger said: "We are thrilled with the huge response from British and Irish audiences."
The film also worked its magic at North American cinemas, taking an estimated $75m (£61m) over the weekend - more than the rest of the US box office top 10 combined.
Harry Potter creator Rowling has planned scripts for a total of five films in the series.
The first instalment is set in New York, and tells the story of a fictional author mentioned in the Potter stories.
Redmayne plays the part of the animal-loving magizoologist Newt Scamander, who visits New York's secret community of witches and wizards.
The film is set 70 years before Harry Potter reads his book at his school, Hogwarts.
It has received broadly positive reviews from critics.
The opening weekend haul in the US and Canada was lower than for any of the Harry Potter films, however.
Elsewhere in the box office charts, Benedict Cumberbatch's Doctor Strange fell to second with $17.7m (£14.3m), with Trolls third on $17.5m (£14.1m).
Sci-fi movie Arrival, starring Amy Adams, took fourth spot with $11.8m (£9.5m), while the comedy Almost Christmas, starring Danny Glover and Gabrielle Union, rounded out the top five with $7m (£5.7m).
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Beth Potter, Laura Muir and Callum Hawkins sealed early places.
Andrew Butchart, Eilidh Doyle, Zoey Clark, Chris O'Hare, Steph Twell, Josh Kerr and Eilish McColgan secured their spots at the British team trials.
Guy Learmonth qualified at the Anniversary Games, while Lynsey Sharp and Jake Wightman were handed team berths by the selectors.
Marathon runner Robbie Simpson had qualified but then withdrew due to a calf injury.
Scotland's previous best total of athletes at the worlds was seven, achieved in 1983 and 2015.
The number of Scots represented reflects a recent improvement in the results of the nation's athletes.
Middle-distance runner Muir is leading the way, having set five British and two European records in the past year. She will go in the 1500m and the 5,000m.
O'Hare, who runs in the 1500m, is another Scot to watch, following a great season that included victory at the British Team trials and the Anniversary Games. Kerr, who finished second at the trials, joins O'Hare in the team, with Wightman also selected after finishing third at the trials.
Doyle will be competing at her fifth World Championships as she goes in the 400m hurdles, while Aberdeen's Clark will sample her first major championships having earned her spot in the 400m.
Learmonth will be racing in his first World Championships, having finished second in the 800m at the British trials and secured the qualifying time at the Anniversary Games.
Butchart will be up against Mo Farah in the 5,000m.
"First of all let me firmly congratulate the athletes, their families, their coaches and the clubs involved in their development on selection by GB and NI for a World Champs," said Rodger Harkins, performance director with Scottish Athletics.
"We should never be under the impression that selection for a British team at this level comes lightly. It comes after many years of hard work and dedication, sacrifice by athletes and families, and strong commitment, guidance and experience from coaches.
"Looking through those selected, I can see examples of that in each and every one of those 13 Scottish names."
Harry Potter spin-off Fantastic Beasts and Where To Find Them has had the biggest UK box office opening weekend of the year so far.
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Scotland will have 13 athletes at the London 2017 World Championships - almost double the previous best total.