As DP and others have mentioned, swaddling usually works and is easy to do. Just fold the two diagonal corners of blanket together and then place your baby with their feet at the narrow end and their head at at the large end, tuck in one corner over the one arm then the other. You can do this before picking them up to so when he settles he can be put right back into the Moses basket. You can also put an old clock near the top of the basket as the ticking simulates a heart beat.
Also important, get your partner to put a top she has recently worn into the basket near the top of the basket (or even better wrap the clock inside) as this will then allow your child to smell her as well. All this goes at the top of the basket and the baby must be pushed towards the bottom of the basket to stop him sliding under his blanket.
Remember to not let him sleep in the same position all the time. Get a cushion that holds him in place and rotate him from sleeping on the left then the back then the right side to prevent torticollis and developing a flat skull.
Good luck and enjoy Parenthood. Amazing things, kids