Goodby recently dropped out of the running for Volvo's £75m global account in February to focus on winning the Hyundai pitch.
Joel Ewanick, Hyundai Motor America marketing vice-president, said: "Hyundai is committed to making further major steps in improving its brand image and increasing sales in the United Sates.
"We believe that the superb strategic thinking and creative executions that we have seen from Goodby, Silverstein & Partners will take Hyundai Motor America to a much higher level"
Hyundai's account was previously held by the independent agency the Richards Group in Dallas since 2002. It parted company with the automotive firm in February.
Jeff Goodby, co-chairman of Goodby, Silverstein & Partners, said: "We are thrilled and honoured to work with Hyundai at this very important time for their brand. There is a great opportunity to share their fantastic product stories and push their momentum even further."
This account is the second recent major account gain for Goodby. At the start of this month, , the third-largest mobile phone company in the US, chose the agency to create its consumer and business advertising.