While the PGA Tour Champions, formerly known as the Senior PGA Tour, has only been around since 1980, senior major championship golf dates well back into the 1930s with the advent of the Senior PGA Championship. Nowadays, the PGA Tour Champions has five major championships -- the Regions Tradition, Senior Players Championship, Senior PGA Championship, US Senior Open and Senior British Open Championship. Of course, every senior major winner is over 50 years old, but there have been some major winners who have been over age 60 when they hoisted a senior major title.
However, being the oldest winner of a senior golf major and being the oldest winner of a PGA Tour Champions major is two separate records. That's because PGA Tour Champions doesn't formally recognize any win in what's now a senior major before 1980, with the Senior PGA Championship and US Senior Open winners recognized since the tour's founding. The Senior Players came along in 1984, with the Tradition starting in 1989. The Senior British Open Championship was recognized as the fifth PGA Tour Champions major in 2003.
The Senior PGA Championship, however, was first played in 1937 (at Augusta National!) but wins before 1980 do not count toward the record. The Senior British Open Championship started in 1987, but wins before 2003 do not retroactively count as major championship wins either.
So, that means the oldest winner of a PGA Tour Champions major is Bernhard Langer, when he won the 2017 Regions Tradition at 59 years, 8 months, 24 days.
However, the oldest winner of a senior major championship is Jock Hutchison, who won the 1947 Senior PGA Championship at 62 years, 7 months, 5 days old. The second-oldest winner of a senior major is Gary Player, who won the 1997 Senior British Open Championship at 61 years, 8 months, 26 days.