The obituary was given by Jesse Paris Smith, daughter of Patti Smith, another rock icon from the same city.
He died aged 73 after a short illness.
Tom Verlaine died surrounded by those closest to him in New York.
Television is best known for the album "Marquee Moon" (1977).
The band disbanded already in 1978, but reunited several times.
The late legend was originally named Thomas Miller.
He took the stage name from the French poet Paul Verlaine.
Collaborated with Patti Smith
Tom Verlaine and his schoolmate Richard Hell formed the group Neon Boys in 1972.
The following year it was reformed into Television with Richard Lloyd as the new guitarist.
Their first gig was in March 1974 and Television became one of the most important groups in 1970s New York along with the Ramones, Blondie, Talking Heads and Patti Smith with whom Tom Verlaine also worked.
After the band split in 1978, Tom Verlaine released several solo albums, the most recent in 2006. He also collaborated with, among others, David Bowie and the 1980s band Violent Femmes.
One of those who was inspired by Tom Verlaine's music is Billy Idol.
On Twitter he writes:
“He made incredible music that influenced the punk rock scene in both the US and the UK in the 70s.
RIP”
Compared to Hendrix
“Tom Verlaine has gone beyond what his guitar playing always gossiped about.
He was the greatest rock and roll guitarist of all time, and like Hendrix he could dance from the realms of the cosmos to garage rock.
It takes a special kind of greatness," writes Mike Scott from Waterboys on Twitter.
And the tributes on social media come from several quarters:
"Tom Verlaine's playing meant everything to me.
He was the one who made me become a guitarist," writes Will Sergeant, guitarist in Echo & The Bunnymen.
"Peace and love, Tom Verlaine" followed by a broken heart, writes Susanna Hoffs from The Bangles.
“He was my guitar hero at a time when I needed him the most.
"I spent all of 1981 practicing playing 'Marquee Moon' daily," Dream Syndicate guitarist Steve Wynn wrote on Twitter.