The others, Mufid Abdulqader, the brother of Hamas political leader Khaled Meshaal, and Abdulrahman Odeh, the charity's New Jersey representative, were convicted on three counts of conspiracy.
Odeh was sentenced to 15 years while Abdulqader, the foundation's fundraiser, received 20 years.
"I do acknowledge the verdict in this trial," Abdulqader said during the sentencing hearing.
"I believe in the system. My faith has not been shaken, it's been inspired. But it is un-American to ignore suffering and starving women and children."
Abu-Baker and Elashi were convicted of a combined 69 charges, including supporting a specially designated "terrorist" organisation, money-laundering and tax fraud.
Abdulqader and Odeh were convicted on three counts of conspiracy.
The Holy Land Foundation, once the largest Muslim charity in the US, was itself convicted on all 32 counts.
An earlier trial ended in October 2007 with one man acquitted on 31 charges but jurors unable to agree on verdicts for others.
Prosecutors said the charity was spreading Hamas's ideology by funding schools, hospitals and social welfare programmes controlled by the group in the Palestinian territories, and permitting it to divert funds to the activities of fighters.
The charity's supporters countered that the government was politicising the case as part of its so-called war on terror and ignoring the foundation's charitable mission in providing aid to the poverty-stricken Palestinian territories.
Government officials had raided Holy Land's headquarters in December 2001, and George Bush, the then US president, later announced the seizure of the charity's assets as "another step in the war on terrorism".
But defence lawyers said their clients had been put on trial partly because of their family ties to members of Hamas, such as Abdulqader's brother Meshaal, who is in exile in Syria.
As grounds for an expected appeal, lawyers for the men are expected to challenge testimony given by an anonymous Israeli government agent, whose evidence was kept secret from the defence.