Born in Tokyo, Katayama raced in France for three years before returning to Japan in 1988. He scored three podiums in the Japanese F3000 championship in 1990 and won the title in 1991 with two victories and three second places.
Japan Tobacco arranged a Formula One seat for Katayama at Larrousse in 1992 under the Cabin cigarette brand. The car was unreliable and a clear midfield runner, with teammate Bertrand Gachot holding a larger share of team resources. Katayama impressed by running fifth at the Canadian Grand Prix before his engine failed; he ultimately finished the year with a pair of ninth places as his best results.
Japan Tobacco secured a move to Tyrrell for 1993, but the team was at a low ebb with an ageing interim car. Tenth place at the Hungarian Grand Prix was his best result that year.
The 1994 season brought a significant turnaround. Katayama impressed with the new Tyrrell 022, outpacing more experienced and acclaimed teammate Mark Blundell on several occasions and putting in strong qualifying performances. He was consistently a top-six runner but suffered 12 retirements from reliability failures. A highlight and a heartbreak arrived at the German Grand Prix, where he was running third before a stuck throttle forced him out. In the four races he finished, he scored two fifth places, one sixth, and one seventh, totalling five championship points.
After 1994, it was reported that Benetton offered Katayama a seat for 1995 alongside newly crowned World Champion Michael Schumacher. He could not accept; it later emerged he had been diagnosed with cancer in his back during 1994. The condition was not immediately life-threatening but was painful, and his race schedule delayed treatment. He chose not to announce the diagnosis at the time, refusing to let it become a reason for poor results.
Katayama remained at Tyrrell for 1995 and 1996 but his form dropped, and he was outpaced by rookie teammate Mika Salo. Regulation changes after Ayrton Senna's death at the 1994 San Marino Grand Prix mandated higher cockpit sides that Katayama found particularly restrictive. At the 1996 Belgian Grand Prix he finished on the lead lap for the only time in his career.
Japan Tobacco's Mild Seven brand placed Katayama at Minardi for 1997, but the team was similarly uncompetitive. Two tenth places were his best results. At the Japanese Grand Prix — his home race — he emotionally announced his retirement from Formula One.
After Formula One, Katayama moved into sportscar and GT racing. At the 1999 24 Hours of Le Mans he shared a Toyota GT-One with Keiichi Tsuchiya and Toshio Suzuki. During the final hour, while closing on the leading BMW, a tyre blowout forced him to crawl back to the pits. The car lost its chance to fight for the overall lead and finished second overall, though it won the GTP class as the only finisher in that category.
Katayama established Team UKYO in 2000. The team participated in the Japanese GT Championship in 2001 and 2002 and returned in 2011 to lead Goodsmile Racing's GT300 programme, winning the GT300 class title in 2011, 2014, and 2017. The team also contested the Dakar Rally between 2002 and 2007. From 2012, Team UKYO has operated as a UCI Continental road cycling team.
Away from motorsport, Katayama is an accomplished mountaineer. He has summited six of the Seven Summits: Mont Blanc, Kilimanjaro, Elbrus, Denali, Aconcagua, and Vinson Massif. In December 2009 he survived an incident on Mount Fuji in which two climbing companions died. He has served as a Formula One commentator for Fuji TV in Japan.