Born in Copenhagen, Tverskov started playing football at the age of three at Boldklubben 1903 (B 1903).
As a 17-year-old, he was promoted to the first senior team competing in the fourth-tier Denmark Series by the then manager Bent Christensen.
In his first season, he made 24 appearances and seven goals, and was voted Player of the Year at the club.
1990
He came on as a 90th-minute substitute for David Boysen, as his team won 2–1.
1993
Jeppe Theis Tverskov (born 12 March 1993) is a Danish professional footballer who plays as a centre back for Nordsjælland.
2011
In June 2011, Tverskov moved to Lyngby Boldklub on the recommendation of his manager, Bent Christensen.
At that club, he played alongside fellow youngsters such as Yussuf Poulsen, Christian Nørgaard and Uffe Bech.
2012
In June 2012, he was promoted to the first-team by head coach Niels Frederiksen.
Tverskov made his first professional appearance on 4 November 2012 against Hobro IK in the second-tier Danish 1st Division.
2014
He scored his first professional goal on 25 April 2014, during a 0–3 league victory for his team over Hvidovre IF.
On 30 June 2014, Tverskov joined Randers, where he signed a two-year contract.
He played his first match for the club on 23 September in a Danish Cup match against Kolding Boldklub.
He started the match as a defensive midfielder and stood out by also scoring his first goal for Randers, thereby participating in his team's 1–7 win.
The club finished fourth in the Danish Superliga at the end of the 2014–15 season and managed to qualify for the qualifying rounds of the UEFA Europa League.
2015
Tverskov played his first European match in this competition, on 2 July 2015 against Andorran club UE Sant Julià.
He appeared as a starter, but was however sent off after receiving a second yellow card, as Randers won 1–0.
2016
As his contract expired with Randers, Tverskov signed with Odense Boldklub (OB) in the summer of 2016, the transfer being announced on 20 April of the same year.
He made his first appearance for the club on the first matchday of the 2016–17 Superligaen season, against SIlkeborg.
That day, he started the match, which ended in a 0–0 draw.
In June 2023, Tverskov signed for Nordsjælland until June 2025.
