Shein, of the ruling Chama Cha Mapinduzi (CCM) party, welcomed the announcement, a day after the presidential and legislative vote which was boycotted by the opposition.
"I am prepared to serve Zanzibaris for another five years. Let's work together," said Shein, who has been in power since 2010 and is due to be sworn in again on Thursday.
Sunday's presidential and legislative elections were a re-run of October polls that were cancelled by the ZEC over fraud allegations.
Shein won just over 91 percent of the vote, according to Zanzibar Electoral Commission (ZEC) chairman Jecha Salim Jecha.
Hamad was first vice president in the unity government that ruled Zanzibar from 2010 but said he would not participate in any future administration.
Almost 68 percent of Zanzibar's 503,000 registered voters turned out on Sunday, according to the ZEC.
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