The two men received a welcome from ministers, political leaders and other dignitaries at the VIP lounge of Sana'a International Airport on their arrival on Tuesday.
The 61-year-old scholar was greeted by a roaring ovation from crowds and his motorcade was brought to a virtual standstill several times by screaming crowds.
He also received the welcome of President Ali Abdullah Saleh at the presidential palace following his arrival in the city, the official Saba news agency reported.
The pair were released after their lawyer struck a plea bargain deal with US prosecutors, sources close to the family of al-Moayad told the German Press Agency dpa.
Under the agreement, the men pleaded guilty to providing aid to Hamas, which is listed among terrorist groups by US government, and were sentenced to six years time served.