The four - three men and a 24-year-old woman identified as Denise Vanessa G. - were arrested in May 2015, two days before they planned to strike at the migrant shelter in the eastern state of Saxony.
Known as the "Old School Society", their choice of weapon was modified "pyrotechnic explosives, particularly in the form of fire and nail bombs", which they were planning to hurl into a refugee home, the prosecutor had said.
The group had therefore "accepted that people could be killed," chief prosecutor Jörn Hauschild had told the court.
The ringleader Andreas H., 58, was sentenced to four and a half years in prison while his second-in-command Marcus W., 41, got five years.
The group's "spokesman" Olaf G., 31, was given three years while the only woman obtained three years and 10 months.
The sentences were however more lenient than the four and a half to seven years sought by the prosecutor.
The four met on the internet in 2014.
In preparation for the attacks, they bought large quantities of banned fireworks from the Czech Republic and subsequently decided to cover the explosives with a layer of nails to make them more lethal.
Hauschild described their plan for the Saxony attack as very concrete, adding that the authorities had learned the details from chat logs and phone intercepts.
Media websites show group emblems popular in the neo-Nazi scene, such as bloody hatchets and skulls with the slogan: "One bullet is not enough."
Amateur videos posted on YouTube and attributed to the group also use racist and xenophobic slurs in appeals for new recruits.
A record influx of asylum seekers to Germany has fuelled a sharp rise in the number of far-right attacks, with Saxony state gaining special notoriety for such violence.
In 2016, there were about 3,500 attacks against refugees and asylum seekers in Germany - ten each day, on average - injuring 560 people including 43 children, interior ministry data show.
Saxony, with just five percent of the German population, was the scene of 437 attacks last year, according to the RAA, a victims' assistance organisation, after 477 in 2015.
Another extremist group in Freital, Saxony is currently on trial for five different attacks targeting refugee homes and left-leaning politicians. The seven men and one woman face charges of starting a terror cell, attempted murder, causing grievous bodily harm, causing explosions and property damage.