Capela, whose parents are from Angola and the Congo, was born in Geneva, Switzerland. His parents separated a few months after his birth, leaving his mother to raise him and his brothers by herself. His passion as a youngster was football, but due to being 1.90 m (6 ft 3 in) as a 13-year-old, his eldest brother suggested he switch to basketball. At 15 years old, he was spotted at the European Junior Championships with the Swiss team and joined the Chalon-sur-Saône training center, INSEP, in France.
In 2012, Capela joined the senior Élan Chalon team of the LNB Pro A.
On April 12, 2014, Capela represented the World Team at the 2014 Nike Hoop Summit. Later that month, he declared for the 2014 NBA draft. In May 2014, he was named the Best Young Player and Most Improved Player of the 2013–14 LNB Pro A season.
On June 26, 2014, Capela was selected with the 25th overall pick in the 2014 NBA draft by the Houston Rockets. On July 25, 2014, he signed with the Rockets. On March 30, 2015, Capela scored his first NBA points, finishing the game with eight points and nine rebounds in a 99–96 loss to the Toronto Raptors. On April 13, he had a season-best game for the Rockets with 10 points and five rebounds in a win over the Charlotte Hornets. During his rookie season, he had multiple assignments with the Rio Grande Valley Vipers of the NBA Development League. Capela took a step forward in the postseason, when he saw minutes in place of the injured Donatas Motiejūnas. He appeared in more playoff games (17) than regular season contests in 2014–15 and averaged 3.4 points in 7.5 minutes per postseason game.
On November 6, 2015, Capela recorded his first career double-double with then career highs of 13 points and 12 rebounds as a starter in a 116–110 win over the Sacramento Kings. On November 29, in an overtime win over the New York Knicks, Capela recorded his third double-double over a span of four games, including a career-high 18 points. During the 2016 NBA All-Star Weekend, Capela competed for the World Team in the Rising Stars Challenge. On April 13, in the Rockets' season finale, Capela recorded a career-high 17 rebounds in a 116–81 win over Sacramento.
On November 19, 2016, Capela scored a career-high 20 points in a 111–102 win over the Utah Jazz. On December 19, 2016, he was ruled out for six weeks after suffering a broken fibula. He returned to action on January 17, 2017 against the Miami Heat after missing 15 games; he started the game against Miami but was scoreless in nine minutes.
In August 2013, Capela debuted for the Swiss national basketball team at the FIBA EuroBasket 2015 qualification rounds.
Note: The EuroLeague is not the only competition in which the player participated for the team during the season. He also played in domestic competition, and regional competition if applicable.Regular season