Formal:
* "Thank you for accepting me into your circle of friends. I truly appreciate your friendship."
* "I am grateful for your acceptance and the opportunity to be your friend."
Informal:
* "Thanks for being my friend. I'm really glad you accepted me."
* "It means a lot to me that you're willing to be friends. Thanks!"
* "I'm so happy to be friends with you. Thanks for saying yes!"
More heartfelt:
* "I'm so lucky to have you as a friend. Thank you for being so kind and welcoming."
* "Your friendship means a lot to me. I'm so grateful you're in my life."
Humorous:
* "I'm glad you didn't run screaming! Thanks for being my friend."
* "High five! You're stuck with me now." (Only if it fits your relationship)
Remember to choose the expression that best fits your relationship with the person and your personal style.