England were nominated as the chosen home nation to represent GB in the qualification events, and the women’s team beat France to reach the final.
They then saw off hosts Russia 19-0 in Kazan to win the tournament.
In the men’s event in Colomiers, England also faced the hosts in the final, beating France 31-7.
Having finished second in their group on Saturday, the women’s team overcame Ireland 17-7 in the quarter-finals
In that match, England trailed but Holly Aitchison replied on the stroke of half-time as they went into the break 7-5 down.
Deborah Fleming went over in the corner to put them ahead, before Matthews sealed victory just before full-time.
In the tense semi-final, Matthews crossed to give England an early lead before France levelled through Coralie Bertrand.
Ellie Kildunne gave England the lead after the break and despite Valentine Lothoz’s try, two conversions from Aitchison took them through 14-12.
Neither side made the breakthrough in the first half of the final, before Heather Fisher squeezed through for the opening try to set England on their way to Olympic qualification, with Emma Uren and Alex Matthews also scoring against the hosts.
“They are still a really young group and it’s so exciting to think what the future holds for them,” coach James Bailey said.
The men’s team beat Italy 35-0 in the last eight after tries from Harry Glover, Tom Mitchell, Will Muir, Ben Harris and Will Edwards.
Dan Norton, Mike Ellery and Muir put England 17-0 ahead at the break in the semi-final against Portugal before Charlton Kerr and Ben Harris also went over in a 29-12 win.
England led France 21-7 at half-time in the final after Norton scored a hat-trick before the break. Ollie Lindsay-Hague’s interception led to a fourth try to settle the contest.
Britain’s women’s team finished fourth when rugby sevens made its Olympic debut at Rio 2016, losing their bronze medal match 33-10 to Canada, while the men won silver after a 43-7 defeat by Fiji in the final.