He began his career with Italian side Cesena in 2013 and was subsequently loaned out to San Marino for two seasons before returning to the club. He joined Sassuolo in January 2016 but spent the rest of the season on loan with his former club Cesena before officially joining the Sassuolo in the summer.
Born in Urbino in the Marche, Sensi started to play football with the local team Urbania at the age of six. During this time at the club, he played with his older brother. While at Urbania, he was spotted by a Rimini scout, joining the youth team in 2007. He spent three years in Rimini, until the end of the 2009–10 season when the club's ownership left. The club was subsequently refounded, but Sensi left the team, taken in by the youth academy of the local rivals Cesena.
Sensi began his senior career with Cesena. He was first included in a matchday squad for their Coppa Italia fourth round game on 28 November 2012, remaining unused in a 3–1 loss to Atalanta at the Stadio Atleti Azzurri d'Italia.
On 23 July 2013, he was one of a quintet of Cesena players who moved to San Marino Calcio, in his case a loan with the option of co-ownership. He made his professional debut on 8 September, playing the full 90 minutes of a 2–0 Lega Pro Seconda Divisione loss away to Reggiana. A week later he scored his first goal, finishing from the edge of the penalty area to conclude a 2–0 win over Como at the Stadio Olimpico. On 16 March 2014, he was one of three Titani players sent off in a 2–0 defeat at Cremonese. He played 26 games in his first professional season, scoring another goal in the last game, a 2–2 home draw with Vicenza on 4 May.
San Marino did not take up the option to obtain Sensi, but on 7 July 2014 he went to the club for a second loan. In his second match of the season, on 8 September, he was sent off in added time at the end of a 2–1 loss at Pontedera. He played 33 games in a season which ended with relegation to Serie D, scoring eight goals, including two in a 3–2 home win over L'Aquila on 14 February 2015, in which he was again sent off at the end.
Sensi made his Cesena debut on 20 August 2015, playing the entirety of their 4–1 win at Catania in the third round of the Coppa Italia. On 5 September, he made his league debut, as the team won 2–0 against Brescia at the Stadio Dino Manuzzi in the first game of the season. On 3 October he scored from a penalty as Cesena defeated Livorno 1–0.
On 13 January 2016 Sensi was signed by Serie A club U.S. Sassuolo Calcio. He would spend the first 6 months of the contract on loan with Cesena.
Sensi has represented Italy at youth level, making one appearance for the under-17 side, and making his debut for the under-20 side in a 2–2 draw against Poland on 7 October 2015.
A former offensive central midfielder, with good vision, tactical intelligence, and technique, Sensi now usually functions in a creative midfield role for his team, as a deep-lying playmaker, due to his vision, range of distribution, and long passing ability with both feet, which allows him to create chances for teammates; he is also capable of playing in several other midfield and offensive positions, and has been deployed as a winger or as a supporting forward. Already regarded as one of the most promising young Italian footballers of his generation, Sensi has drawn the attention of larger clubs, and his playing style, mobility, small stature, and low centre of gravity have drawn comparisons with Marco Verratti, as well as Andrea Pirlo, although he has personally stated that his main influence is Spanish playmaker Xavi. Sensi has also been praised by Inter manager Roberto Mancini, who described him as: "...good, technically gifted, and fast", also noting that "...he has character." In spite of his slender build, which makes him ineffective at winning more physical challenges for the ball, he is also effective defensively due to his interpretation of space.