Lambert signed for his hometown club in a £4m deal after a hugely successful five years at St Mary’s in which he scored 117 goals in 235 games, completing a rags to riches rise from factory worker to England international.
Rodriguez and Lambert forged a great relationship with each-other on the pitch, scoring 17 and 14 goals respectively last term.
But while he’ll be sorely missed at Saints, Rodriguez is immensely happy for the 32-year-old.
“I’m really proud of him,” he said.
“He’s a great guy off the field but on the field he’s just helped me so much. “It’s been great playing with him, so I’m very proud of him.
“I learnt the most off Rickie. It’s a shame to see him go.”
Lambert is currently with Roy Hodgson’s England team at the World Cup in Brazil alongside Adam Lallana and Luke Shaw, who have both been linked with moves.
The 24-year-old, whose World Cup hopes faded with a ruptured cruciate ligament in early April, will be watching his friends from the sofa.
“I’m rooting behind all of them,” he said.
“They’re representing England and I’m sure they’ll do really well.
“I’m just looking forward to seeing them out there playing.
When asked how far he thinks England will go in the World Cup, he said: “There are no limits for them. “It’s hard to put a prediction on it but you look at the squad and the managerial staff there, they can go as far as they want.
“They’ve (Lallana, Lambert and Shaw) have done really well and they each deserve their place.
“Fingers crossed, I’ll get to see them play lots out there.”