The 27-year-old forward was a free agent, having recently left Hull City when his contract expired.
He spent four years with the Tigers, making 118 appearances for them and scoring 15 goals.
Aluko, who can play on the wing or through the middle, represented England at youth level and has since won seven caps for Nigeria.
He began his career at Birmingham City and played in Scotland for Aberdeen and then Rangers before joining Hull.
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Henrikh Mkhitaryan's sublime solo goal proved the difference as second-placed Dortmund moved within five points.
The Armenia captain ran at the away defence from deep before firing into the bottom corner from 20 yards.
Pep Guardiola's side can restore their eight-point lead with a win at relegation battlers Augsburg on Sunday.
Bayer Leverkusen moved into third when they fought back from behind to win 2-1 at Darmstadt, while Hertha Berlin dropped to fourth after losing 2-0 at Stuttgart.
Second-bottom Hoffenheim, with new 28-year-old manager Julian Nagelsmann taking charge for the first time, drew 1-1 at relegation rivals Werder Bremen.

The company said that Kensington and Chelsea had seen prices plummet by 16% since a peak in September 2014.
In Westminster it claimed there had been a fall of 22% between a peak in November and the end of May.
It blamed the fall on the new stamp duty regime, introduced in December, which penalises expensive properties.
Based on average prices, anyone buying a property in Kensington and Chelsea can now expect to pay more than Â£118,000 in stamp duty alone.
"This fall-off in the top tiers of the market has cooled activity levels too," said Adrian Gill, director of Reed Rains and Your Move estate agents, part of the LSL group.
He said the number of homes being sold in London as a whole had dropped by 16% in the year to April.
A wider survey by the Royal Institution of Chartered Surveyors (RICS) reported that the stock of houses per surveyor has fallen to its lowest level for at least 37 years.
However, prices in the London suburbs - and other parts of England and Wales - continued to hit new highs, said LSL.
According to its calculations, prices rose by 4.5% in the year to May, making the average cost of a home Â£277,178.
That is similar to estimates by the Office for National Statistics, but much higher than figures from Halifax and Nationwide.
Buyers of properties worth less than Â£937,000 now pay less in stamp duty than they used to.
Prices in England's smallest county - Rutland - rose by 23.8% over the year, while those in the Welsh county of Carmarthenshire went up by 16.4%.
Thirteen outer London boroughs saw prices hit new highs.
Previous figures from the Land Registry have suggested that prices in the suburbs across England and Wales have been taking off, including in parts of Manchester.
The separate RICS survey suggests prices in England and Wales could rise by as much as 25% over the next five years, due to the shortage of housing stock.
It said that, away from the South East, the strongest growth was expected in north-west England, as a result of the government's northern powerhouse initiative.
LSL's house price index is based on statistics released by the Land Registry, so includes cash sales.

Police said they were called to Peterhead Academy following an incident involving two boys on Monday afternoon.
The teenager was charged in connection with both possession of a knife and the assault.
He has been reported to the youth justice management unit.
Fulham have signed Sone Aluko on a two-year contract with the option of a further year.
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Borussia Dortmund narrowed the gap on Bundesliga leaders Bayern Munich with a hard-fought win against bottom side Hannover.
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House prices in the smartest parts of London have fallen by up to 22% since last Autumn, according to the property services group LSL.
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A 14-year-old boy has been charged after allegedly being found with a knife at an Aberdeenshire school after an assault.