Can my ex boyfriend move out and take all the furniture he bought for me?

No. Gifts are gifts, and they can't be taken back just because the 2 of you broke up. If he sues youb for the value of the furniture, your texts prove that it was a gift and not a loan that you had to repay.

As a practical matter, it's going to be a lot easier for you if he never takes the furniture in the first place. Depending on your particular situation, it may be appropriate to deny him access to your home.

Property given during a romantic relationship are generally considered gifts. I agree with my colleague, if your ex boyfriend has no right to be in your property, then I would keep him out. Your ex can then try to bring an action against you in an attempt to "recover" the property, but his action should fail because the 3 parts of property becoming a gift have been satisfied. Namely, intent (which can be proven by his texts), acceptance, and delivery (based on the fact that the property is in your house, these last 2 are evident as well.