Birkhead, 34, posted two photos of Smith embracing him and an audio file playing Willie Nelson's song "Angel Flying Too Close to the Ground."
And in a written memorial, he says she called him "her angel" and he called her "my sweet potato."
"Chance brought us together, our love couldn't keep us apart," he writes. "We loved, we laughed, we shared a connection that couldn't be broken, regardless of the challenges. I loved her in life and I will love her long after."
Before Smith's death, however, relations between the two had been acrimonious. Birkhead had sued Smith twice, first seeking a court order to demand that she bring Dannielynn from the Bahamas to California for a paternity test and then accusing her and her companion, Howard K. Stern, 38, of conspiring to misrepresent Stern as Dannielynn's father.
The day before Smith's death, Los Angeles Superior Court Judge Robert A. Schnider had ordered that she submit to a DNA test by Feb. 21. On Friday, Schnider will decide whether a court-ordered DNA sample can be taken from Smith's body to help determine Dannielynn's paternity.
Birkhead's attorney, Debra Opri, tells PEOPLE he is devastated, having lost "the love of his life and the mother of his child."
And indeed, Birkhead writes: "My heart is broken, my tears are endless. She called me her angel, I called her my sweet potato, and every night before we went to sleep, she made me say to her ... GOODNIGHT MY SWEET ANNA BABY."
Visit PEOPLE.com for continued coverage of Anna Nicole Smith as the tragic story continues to develop.