It said the all-cash deal was approved unanimously by the boards of both firms.
The Illinois-based AveXis is involved in clinical studies for the treatment of spinal muscular atrophy (SMA), a rare neurodegenerative disease caused by a defect in a single gene.
"The proposed acquisition of AveXis offers an extraordinary opportunity to transform the care of SMA," Novartis CEO Vas Narasimhan was quoted as saying in a company statement.
"The acquisition would also accelerate our strategy to pursue high-efficacy, first-in-class therapies and broaden our leadership in neuroscience."
The announcement comes less than two weeks after Novartis said it will sell its stake in its consumer healthcare joint venture to Britain's GlaxoSmithKline for $13 billion.
The group said the sale of the 36.5 percent stake will enable it "to further focus on the development and growth of its core businesses."
Novartis in January reported that strong sales of two of its main blockbuster drugs enabled it to turn in a "good operational performance" in 2017.
Net profit climbed by 15 percent to $7.7 billion in 2017 on a one-percent increase in sales to $49.1 billion.