His mother, Edis, was a housewife, while his father, Ugo, worked several jobs, firstly as a hairdresser, then as a tailor, and subsequently in a factory, where he died in a work-related accident on 10 February 1953, when Luigi was nine.

Edis began working as a maid, while Luigi was sent to a strict religious boarding school, where he remained for three years, before finding a job in a lift-factory and beginning to play football; his mother died soon afterwards.

The youngster's promising performances attracted the attention of Cagliari president Enrico Rocca, and he was acquired by the Serie B side the following year for a notable sum of 37 million Lire, at the age of 19; Riva remained with the Sardinian team for the rest of his career.

[2][14][4][5][10][11][15][16][17][18] The following season, Riva made his Serie A debut for Cagliari on 13 September 1964, in a 2–1 loss against Roma, and also helped the club avoid relegation, leading the team to a comfortable sixth-place finish in the table, scoring an encouraging 9 goals in 32 appearances at the age of 20.

This was followed by eleventh, sixth, and ninth place finishes in the league between 1965 and 1968, while Riva also finished as the league's top scorer for the first time during the 1966–67 season with 18 goals, as the club began to build a potential title winning side around their star striker: Riva attracted several notable footballers to Cagliari, and the team during this period featured players such as Enrico Albertosi, Roberto Boninsegna, Ricciotti Greatti, Comunardo Niccolai, Mario Martiradonna, Mario Brugnera, Pierluigi Cera, and Nené.

[14][5] Riva subsequently helped Cagliari to a second-place finish in both the Coppa Italia, behind Roma, and the league, four points behind Fiorentina, during the 1968–69 season, winning the capocannoniere title for a second time with 20 goals in 29 appearances.

[14][5] Following the arrival of fellow forwards Angelo Domenghini and Sergio Gori from Inter in the summer of 1969, in exchange for Boninsegna, Riva finally won his maiden career Serie A title with Cagliari during the 1969–70 season.

Under the guidance of manager Manlio Scopigno and his offensive tactics, Riva led the team's front line, scoring several decisive goals that ultimately helped the club win the championship.

On 12 April, Riva opened the scoring with a diving header in an eventual 2–0 win over Bari at the Stadio Amsicora, while Juventus suffered a 2–0 defeat to Lazio in Rome, with goals from Gian Piero Ghio and Giorgio Chinaglia.

Despite having already established himself as a world class player, Cagliari struggled in the league during the mid 70s, Riva remained loyal to the Sardinian side, and turned down many bids from larger clubs, in particular from northern Italy.

During his time with Cagliari, he demonstrated his attachment to the club when he refused several lucrative offers from Serie A giants Juventus to remain in the Sardinian capital, despite numerous rumours in the press which stated that he had already signed with the Turin side in exchange for large, record-breaking sums and several of their own players.

[4][11] Following some impressive performances for the Italian youth side,[17] Riva made his senior international debut with Italy at the age of 20, on 27 June 1965, in a 2–1 friendly defeat against Hungary, coming on for the injured Ezio Pascutti in the eighth minute.

[21] His international career was off to a difficult start, with his performance in his second appearance for Italy, a 0–0 friendly draw against France in Paris on 19 March 1966, criticised by noted journalist Gianni Brera, who initially described Riva as a "one-footed" and "incomplete player".

[10] He was subsequently controversially excluded from the 22-man 1966 FIFA World Cup squad, although he was still brought to England by manager Edmondo Fabbri, along with Mario Bertini, as an additional reserve, to gain experience with the national side; Italy were eliminated in the first round of the tournament.

After recovering from a leg injury, he returned to the starting line-up and scored the opening goal in the twelfth minute of the final replay in Rome on 10 June, which ended in a 2–0 victory over Yugoslavia;[2][4][6][23] Riva was named to the Team of the Tournament for his performance during the match.

On 14 June, he helped Italy defeat the hosts Mexico 4–1 in the quarter-finals, scoring two goals, both from Gianni Rivera assists, forming a notable offensive partnership with the Milan playmaker in the knock-out rounds of the competition.

Due to his height, powerful physique, elevation, and his heading accuracy, Riva excelled in the air, and he also had a penchant for scoring spectacular, acrobatic goals from bicycle kicks, courtesy of his athleticism and volleying ability.

Despite his tall build and strong physical attributes, he also possessed excellent technical ability, creativity, and good dribbling skills, as well as a very delicate first touch and notable elegance on the ball.