The unions gave their conditional backing in letters sent last week to the Federal Trade Commission.
In their letters, SAG-AFTRA and the American Federation of Musicians said they would support the deal if there were adequate mechanisms to ensure that Universal complies with its commitment to re-invest in artist development.
EMI is home to the recorded music of The Beatles, as well as American artists such as Norah Jones and The Smashing Pumpkins. Universal artists include Rihanna, Lady Gaga and U2.
"It has been wrenching to watch EMI wither" as its former private equity owner Terra Firma cut costs, wrote Kim Roberts Hedgpeth, SAG-AFTRA's co-national executive director. She urged regulators to examine Universal's commitments to artist development.
"Should the commission be satisfied that there are adequate mechanisms to ensure compliance with those commitments, we respectfully request that it look favorably on Universal Music Group's stewardship over EMI," she wrote.
Universal said in a statement it was "delighted" that the unions took a positive view of its plans.
In late 2010, Terra Firma defaulted on the $5.5 billion in debt it amassed in its 2007 purchase of EMI. Lender Citigroup foreclosed on the storied recording label in February of last year, and agreed to sell it in two parts for $4.1 billion in November.
Universal, a division of France's Vivendi SA, agreed to buy the recorded music side. A consortium led by Sony/ATV agreed to buy the publishing assets for $2.2 billion.
That has sparked fears of market dominance. On the recording side, the purchase would give Universal about a 40 percent market share in the U.S., towering over Sony Music Entertainment at 29 percent and Warner Music Group Corp. at 19 percent. It will also be among the world's largest music publishers.
Outgoing Warner Music chairman Edgar Bronfman Jr. has called the sale "dangerous" and bad for artists. Independent music labels have also come out against the deal.
The European Commission launched a probe into the acquisition last month, saying that Universal would be nearly twice the size of its next-largest competitor in Europe. The EC has said it will decide by Aug. 8 whether the takeover will impede competition.
Both Sony/ATV and Universal have offered concessions to get the deal done. Universal has said it would sell $660 million worth of non-core assets, mostly minority stakes in companies that it did not disclose.