The 20-year-old, who has represented both England and Scotland at under-19 level, spent the first half of last season on loan at MK Dons.
Gallagher's arrival at the Championship club comes after attacking midfielder Elliott Bennett was ruled out for up to six weeks with a hamstring injury.
Gallagher is available for the league game against Wigan on Saturday.
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Blackburn Rovers have signed striker Sam Gallagher from Premier League side Southampton on a season-long loan.