The extended TeV gamma-ray source ARGO J2031+4157 (or MGRO J2031+41) is positionally consistent with the Cygnus Cocoon discovered by $Fermi$-LAT at GeV energies in the Cygnus superbubble. Reanalyzing the ARGO-YBJ data collected from November 2007 to January 2013, the angular extension and energy spectrum of ARGO J2031+4157 are evaluated. After subtracting the contribution of the overlapping TeV sources, the ARGO-YBJ excess map is fitted with a two-dimensional Gaussian function in a square region of $10^{circ}times 10^{circ}$, finding a source extension $sigma_{ext}$= 1$^{circ}$.8$pm$0$^{circ}$.5. The observed differential energy spectrum is $dN/dE =(2.5pm0.4) times 10^{-11}(E/1 TeV)^{-2.6pm0.3}$ photons cm$^{-2}$ s$^{-1}$ TeV$^{-1}$, in the energy range 0.2-10 TeV. The angular extension is consistent with that of the Cygnus Cocoon as measured by $Fermi$-LAT, and the spectrum also shows a good connection with the one measured in the 1-100 GeV energy range. These features suggest to identify ARGO J2031+4157 as the counterpart of the Cygnus Cocoon at TeV energies. The Cygnus Cocoon, located in the star-forming region of Cygnus X, is interpreted as a cocoon of freshly accelerated cosmic rays related to the Cygnus superbubble. The spectral similarity with Supernova Remnants indicates that the particle acceleration inside a superbubble is similar to that in a SNR. The spectral measurements from 1 GeV to 10 TeV allows for the first time to determine the possible spectrum slope of the underlying particle distribution. A hadronic model is adopted to explain the spectral energy distribution.
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