Ken Tyrrell had sold the team to British American Tobacco prior to the start of the 1998 season, making the campaign a holding year for the BAT-backed transition. Paul Stoddart had come close to buying the team — he had offered a comprehensive three-year development plan including a wind tunnel and the use of his European Aviation company for transportation — but the BAR arrangement had already been finalised. Stoddart's European Aviation nonetheless sponsored the team throughout the season and provided logistical support.
Ken Tyrrell himself departed the team before the first race. His exit was triggered by the driver selection: new team principal Craig Pollock chose Ricardo Rosset as the partner for Toranosuke Takagi, a decision that infuriated Tyrrell, who had wished to retain Jos Verstappen. Pollock's rationale was financial — Rosset brought superior sponsorship money to the team.
The 026 carried over a V10 engine and offered what was described as a reasonable chassis, though the competitive ambition of the year was limited by the knowledge that BAT would be starting from scratch in 1999. The car retained the side-mounted tower wings — introduced by Tyrrell on the 025 — that had been copied by a number of other constructors during 1997. The FIA banned these wings partway through the 1998 season after the San Marino Grand Prix.
The competitive picture was difficult. Rosset failed the 107% qualifying cutoff on five occasions, and his performance at Monaco caused such frustration among the mechanics that they defaced his paddock scooter, rearranging the letters in his surname to spell "tosser." His best result of the season was an eighth-place finish in Canada, which also stood as the team's best result of the year. At one stage Rosset's seat was in danger of being given to Danish driver Tom Kristensen, who tested at Magny-Cours and posted competitive times.
Takagi provided more consistency without ever threatening the midfield leaders. The team recorded no championship points, finishing behind Minardi in the unofficial standings due to the Italian team's superior finishing record.
The two 026 chassis raced by Takagi and Rosset were later acquired by Dutch racing driver and businessman Frits van Eerd, who campaigned them in the EuroBOSS series. Paul Stoddart also purchased a significant portion of the team's assets, including 026 chassis that subsequently formed the basis of his Minardi F1x2 two-seater experience cars.
The 026's completion of the 1998 season brought down the curtain on Tyrrell as a constructor after more than two decades of Formula One involvement, a legacy stretching back to Jackie Stewart's three World Championships in 1969, 1971, and 1973.
The 026 wore a white and black livery continuing the PIAA title sponsorship from 1997, the Japanese company's final year backing the team before switching to Arrows. Silver accents were added for 1998, with orange used to identify Takagi's car and green for Rosset's. PIAA subsequently moved its support to the Arrows team for 1999.