U.S. companies have flooded eurozone bond markets with a record amount of new debt deals this year, a trend that bankers and investors say is likely to continue at a fast pace for the rest of 2015.

Among the long list of U.S. companies that have crossed the Atlantic, Wells Fargo & Co. and American Honda Finance Co. issued bonds in euros last week, together raising more than €2 billion ($2.2 billion), continuing a long string of U.S. financial firms eager to diversify their funding bases.

But...