A vacancy was created in the position after the ousting of Manasseh Sogavare as prime minister in a vote of no-confidence last week
However, Sogavare's group subsequently remained largely intact and was last week joined by a number of opposition MPs including Mr Hou.
The former Finance Minister and Central Bank Governor is the 12th person to be prime minister of Solomon Islands.
The opposing group nominated the Central Honiara MP John Moffat Fugui as its candidate.
Hou won the vote 33 to 16 and will form the next government.
As today's secret ballot vote took place a bolstered police presence deployed around the parliament in case of politically-driven unrest.
Police say they will maintain the extra presence for the next day or so.