The 28-year old joins the Tigers from Stoke on a season-long loan as Turner leaves KC Stadium for Sunderland.
Although Brown was disappointed to lose Turner, he sees Sonko as an apt replacement.
"The Michael Turner deal represents tremendous business as far as we were concerned," Brown told Sky Sports News.
"I've just had a phone call from Michael wishing us all the best and it goes his way as well.
"It's disappointing that you lose one of your best players. He's been a great servant for us for the last two or three years.
"But it's time to move on, and we've brought in Ibrahima Sonko, obviously to try to fill the gap that Michael will leave.
"Hopefully the lad will go on to better himself and get onto the international stage.
"(Sunderland boss) Stevie Bruce has got himself a good character but we believe we've got ourselves a good character as well."