The FTSE 100 clothing retailer said the profits from any sales of the contested designs would be paid to Scamp & Dude, who in turn would donate the proceeds to charity.
The firm added that the remaining clothing bearing the design would be donated to a charity for the distribution of children’s clothing overseas.
The dispute arose in September when the label founder, Jo Tutchener-Sharp, accused Next of “blatant infringement” on a children’s animal top.
"When a company makes £635m a year net profit, surely they have the resources to create their own designs and not take from independent businesses like Scamp & Dude," she wrote in an Instagram post at the time.
"This has to stop. Where has the integrity gone in the fashion industry?" she added.
In late-afternoon trading Friday, Next shares were down 1.5% at 5,398p.