The French artist cut out paper shapes for collages when ill-health prevented him from painting, producing famous pieces such as The Snail and Blue Nude.
The Daily Telegraph said the London gallery must know it has a "winner" with its "outstanding" exhibition.
"I eat it with my eyes and never feel sated," said The Guardian's critic.
Many of the items will be seen together for the first time in the exhibition, which opens on Thursday and features about 130 artworks from the latter stage of Matisse's career.
The Telegraph said that "the joy of the cut-outs is their simplicity".
The paper's critic said the artworks were made from "modest materials" using "basic techniques" but that the artist "reduces art to the essentials of colour, shape and pattern".
"Yet precisely because they offer us instant visual gratification, it is easy to forget how innovative they actually are," he wrote.
The Guardian added that the show was "ravishing, filled with light and decoration, exuberance and a kind of violence" adding that it was "about more than just pleasure".
"Matisse created a universe that filled the room around him, spilling from the walls to the floor."
Matisse worked from a wheelchair after treatment for cancer and the exhibition compiles work dating from 1937 to 1954, when he died aged 84 of a heart attack.
Sir Nicholas Serota, the Tate director and co-curator of the show, told the BBC the works displayed great skill.
"Cut-out sounds a bit simplistic, they are very sophisticated objects.
"The brilliance is that he took the method of a child and deployed it with all the sophistication of an artist who had been painting for 60 years."
He said that the artworks were "incredibly influential" on a generation of American painters in the 60s and 70s.
"The colour is really intense, the colour is brilliant, it's really not quite what we associate with the immediate post-war years in Europe. He's really on his own."
The Economic Voice added that the exhibition "re-examines the cut-outs in terms of the methods and materials that Matisse used, and their double lives, first as contingent and mutable in the studio and ultimately as permanent works through mounting and framing".
The exhibition will be at the London gallery until 7 September before it travels to New York's Museum of Modern Art in mid-October. It can also be seen by cinema-goers from 3 June with the launch of Matisse Live.
Critics have praised one of the largest collections of Henri Matisse's "cut-out" artworks ever assembled, for an exhibition opening at Tate Modern.