Born in Berekum, Brong-Ahafo, Badu began his career at local club Berlin F.C. before later signing for Berekum Arsenal. Badu was announced in the Ghana Premier LeagueAll Star Team on 21 May 2007. On 11 July 2008, Badu left Berekum Arsenal, signing a one-year loan contract with Asante Kotoko. Badu had trials in England with Middlesbrough in August 2008 and at Wolverhampton Wanderers three months later. Badu then signed on 16 April2009 a six-month loan contract with Recreativo de Huelva, on loan from Berlin FC. Reuters quoted a source from a Berlin FC official, that the loan cost Recreativo about €30,000, while Associated Press reported his new club holds an option for a contract between 30 June2012 and the loan would be effective until the opening of 2009 summer transfer window. His contract with the Spanish club Recreativo de Huelva was dissolved in September 2009 and he moved back to Asante Kotoko.
Udinese
In November 2009, BBC and Sky Sports announced the Italian Serie A side Udinese Calcio would sign Badu in January 2010 and on 28 January 2010, the Udine club announced on its official site the permanent signing of the player from Berlin FC. Badu received his first first team call-up against A.C. Milan on 12 February, but did not play. After a successive "appearances" as unused sub, he replaced Paolo Sammarco on 28 March 2010 against Fiorentina, which Udinese lost 1–4. Badu became a regular in 2011–12 season, replacing departed Gökhan İnler in new 4–1–4–1 or 4–4–1–1 formation against Arsenal. Badu was one of the cover of attacking midfielder Giampiero Pinzi along with countryman Kwadwo Asamoah. In August 2017 he joined Turkish Süper Lig club Bursaspor on loan for the 2017–18 season. He was injured whilst on loan, and returned to first-team action with Udinese in March 2019, after 11 months out.
Verona
On 13 July 2019, Badu signed to Hellas Verona on loan with an obligation to buy. He was hospitalised in August with blood clots on his lungs, but was cleared to play in December 2019.
International career
Badu has represented Ghana at under-20, under-23 and senior level. On 22 May 2008, he received his first call-up to the Black Stars. Badu's first senior international appearance came on 8 June 2008 against Lesotho and his first goal against Congo in June 2011.
In 2010, Badu was selected for his first Africa Cup of Nations as the Black Stars finished runners-up to Egypt, and went on to appear in the 2012 and 2013 editions of the tournament, with the team twice recording fourth-placed finishes. During the 2012 Africa Cup of Nations, in a group match between Ghana and Guinea, Badu flipped up a teammate's pass from just outside the penalty area and launched a mid-air volley to score a goal that was later nominated for the 2012 FIFA Puskás Award. After missing the 2010 FIFA World Cup through injury, Badu was selected in Ghana's squad for the 2014 tournament.
