The aim of this work is to use gamma-ray burst supernovae (GRB-SNe) as cosmological probes to measure the Hubble constant, $H_0$, in the local Universe. In the context of the Expanding Photosphere Method (EPM), I use empirically derived dilution factors of a sample of nearby SNe Ic, which were derived in Paper I of a two-paper series, as a proxy for the dilution factors of GRB-SNe. It is seen that the dilution factors as a function of temperature in $VI$ display the least amount of scatter, relative to $BVI$ and $BV$. A power-law function is fit to the former, and is used to derive model dilution factors which are then used to derive EPM distances to GRB-SNe 1998bw and 2003lw: $36.7pm9.6$ and $372.2pm137.1$ Mpc, respectively. In linear Hubble diagrams in filters $BVR$, I determine the offset of the Hubble ridge line, and armed with the peak absolute magnitudes in these filters for the two aforementioned GRB-SNe, I find a (weighted average) Hubble constant of $bar{H_{0,rm w}} = 61.9pm12.3$ km s$^{-1}$ Mpc$^{-1}$ for GRB-SNe located at redshifts $zle0.1$. The 20% error is consistent with the value of $H_0$ calculated by Planck and SNe Ia within 1$sigma$. I tested the fitting method on five nearby SNe Ic, and found that their EPM distances varied by 18-50%, with smaller errors found for those SNe which had more numerous usable observations. For SN 2002ap, its EPM distance was overestimated by 18%, and if the distance to SN 1998bw was similarly over-estimated by the same amount, the resultant value of the Hubble constant is $H_0 = 72$ km s$^{-1}$ Mpc$^{-1}$, which perfectly matches that obtained using SNe Ia. [abridged]
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