After graduating from BYU, Tavernari signed a 3-year deal contract with
Pallacanestro Biella. During his first season, 2010-2011, he did not play, due to transfer issues. At the end of the season, Jonathan received his Italian Citizenship, due to his father's heritage. In the 2011-2012 season, Tavernari started the season with Biella, playing well in the preseason games, and appearing a few times in the Italian League, Serie A. In January,
Pistoia Basket 2000 acquired Jonathan in a loan from Biella for the remainder of the season. On his debut for Pistoia, Jonathan had a brilliant start, going for 16 points and helping the Tuscan team to a home win against LegaDue's Imola. From January to May, Pistoia and Jonathan were neck to neck with Reggio Emilia to win the coveted promotion prize to the first division. Pistoia came up short, and had to try to win the second guaranteed spot through the playoffs. Pistoia lost to Brindisi in the finals, despite Jonathan's incredible performances in the playoffs against Veroli and Scafati. The head coach for Brindisi,
Piero Bucchi, mentioned after the game that Jonathan was the best 6th man in the league, and for sure would be part of his All-League Team. Tavernari was selected as the 2012 6th Man of The Year for the Italian League. In July 2012, Tavernari signed a 1+1 year-deal with Scafati. In June 2013, JT signed a one-year deal with
Esporte Clube Pinheiros, a professional team in São Paulo, Brazil, and the club he grew up playing for.
Pinheiros participated in the São Paulo League, the
Novo Basquete Brasil,
FIBA Americas League, and the
World Cup for Clubs against
Olympiacos, coming in 2nd place. In July 2014, he then moved back to Europe, to play for
Derthona Basket. For the 2015-2016 season, Tavernari remained in Italy, signing with Agropoli. There he led the newly promoted team to the second best record of the season, being one of the three main players along with Marc Trasolini and Terrence Roderick Jr. The Dolphins were poised for a long post season run, when Tavernari fractured his right foot and missed the remainder of the season. Following his year in Agropoli, JT signed with perennial European contenders Mens Sana Siena. On July 6, 2018, Tavernari signed a 1-year contract with
Lega Basket Serie A (LBA) powerhouse
Dinamo Basket Sassari. After strong performances and a great positive presence within the locker room, Dinamo extended Jonathan's contract until 2020. On July 17, 2018, Tavernari left Sassari after one year and signed with the Italian club
Pallacanestro Cantù. Midway through the 2018-2019 season, Tavernari forced a trade from Cantù back to Scafati, due to financial problems from the Brianzolo team. Jonathan finished the season with a 20 points performance going 6–11 from long range. He averaged 40% from behind the arc that season. ==National team career==