Drill a hole through an interior wall of the laundry room in a spot that's away from all power or plumbing lines and is at least 2 feet off the exterior ground. Drill the hole with an 8-inch bit.
Drill a 4 1/8-inch hole into the exterior wall from outside the house, at the location of the small hole.
Apply caulk around the back side of the vent cap from your vent assembly. Slide the tube through the hole, until the back of the vent cap sits against the exterior wall, sealed by the grout. Caulk around the perimeter of the cap where it meets the wall.
Caulk around the perimeter of the tube inside the laundry room where it comes out of the wall, sealing off that line.
Hook a vent hose to the tube, securing it with a clamp belt. Run the hose to the dryer. Secure it to the dryer's vent tube with a clamp belt.