The singer gave birth to the couple's first child Maxwell Drew on May 1 in Los Angeles.
The baby is said to have created an instant bond with her American footballer father.
"Eric is amazing. He is involved with every single thing, and Maxwell adores him," a source told People.
"Whenever she cries, he picks her up and holds her in his arms, and she immediately stops crying. It's the cutest thing."
The source added: "He is the best dad already. He is also super attentive and taking amazing care of Jess. It's incredible."
Jessica Simpson is said to be "doing great" as a first-time mother and is recovering well.
The birthing suite which Simpson used was rumoured to have cost $4,000 (£2,500) per day.