To synthesize glycogen two enzymes are needed:

1.  UDP-glucose   pyrophosphorylase catalyzes the synthesis of UDP-glucose from UTP and glucose 1-phosphate:

The   pyrophosphate    (PPi)    is   right away hydrolyzed by inorganic pyrophosphatase, releasing energy.  Thus the whole reaction is very exergonic and essentially irreversible.

2.  Glycogen synthase now transfers the glucosyl residue from UDP-glucose to the C4 OH group at the nonreducing end of a glycogen molecule, forming a α1-4 glycosidic bond. Amusingly, glycogen synthase can only extend an existing chain.  Thus  it  needs  a  primer;  this  is  a  protein  called as glycogenin.  Glycogenin  holds  eight  glucosyl  units  linked  via α1-4  link- ages,  which  are  added  to the  protein  by itself  for instance  Autocatalysis.  It is this molecule   which   glycogen   synthase   then   extends.   Each   glycogen   granule have only a single glycogenin molecule at its core. The reality that glycogen synthase is fully active only when in contact with glycogenin limits the size of the glycogen granule.