The bassist and founding member of the group passed away at his home on Hawaii at the end of last week.
The Scots-born musician said Cornick's contribution to the legendary band, renowned as one of the biggest bands of the prog rock era, had been "considerable".
Writing on the Jethro Tull website, he said Cornick's broad knowledge of music helped establish the arrangements of the band's early material. "Glenn was a man of great bonhomie and ready to befriend anyone - especially fellow musicians," he said.
"Always cheerful, he brought to the early stage performances of Tull a lively bravado both as a personality and a musician."
Cornick was the band's original bassist, playing from its inception in 1967 until he left three years later.
After leaving Jethro Tull, Cornick formed his own band, Wild Turkey, and was later a member of Paris with the American guitarist Bob Welch.
Anderson, 67, who was born in Dunfermline and now lives in Wiltshire added: "During the many years since then, Glenn continued to play in various bands and was a frequent guest at Tull fan conventions where he would join in with gusto to rekindle the musical moments of the early repertoire. We will miss him hugely and our condolences go to his wife Brigitte and children."
Cornick had been suffering congestive heart failure and died at home in Hilo on Friday. His son Drew said he had been receiving hospice care before he died. He said his father was brilliant and cantankerous until the day he died.
Cornick played on the band's first three albums -This Was, Stand Up, and Benefit - and their biggest hit Living in the Past.