Ouseph, 30, became the first Englishman in 27 years to win the men's singles title with a narrow 21-19 21-19 victory over home favourite Anders Antonsen.
The husband-and-wife Adcocks beat Danes Joachim Fischer Nielsen and Christinna Pedersen in the mixed doubles final.
Scot Kirsty Gilmour lost in the women's singles final to Carolina Martin.
The Spanish top seed triumphed 21-14 21-12.
It is the first time England have won two golds at the Euros since 1988, when Darren Hall won the men's singles and Gillian Clark claimed the mixed doubles title with Danish partner Steen Fladberg.
The success at the Euros comes after GB Badminton had all its funding cut by UK Sport before the 2020 Tokyo Olympics.
Ouseph, who had previously won two bronzes and a silver in the men's singles at the European Championships, is just the third Englishman to win the event with Steve Baddeley the previous player to triumph in 1990.
Between the wins for Baddeley and Ouseph, players from Denmark had won gold in eight out of nine European Championships.
The second-seeded Adcocks took full advantage of their first appearance in a Euros final to see off top seeds Nielsen and Pedersen, who had won the event in the past two Championships.
The Adcocks were pegged back after winning the first set but held their nerve to triumph 21-17 18-21 21-19.
England claimed two gold medals as Rajiv Ouseph and Chris and Gabby Adcock triumphed in finals at the European Badminton Championships in Denmark.