Baxter has cited work commitments as the reason behind his decision to relinquish the reins at Scatcherd Lane, with the experienced Nuttall taking over for the rest of the season as captain.
Baxter will continue as a player, but believes now is the right time to step down.
He said: “This is my fifth season and it is quite a long stint as skipper and with a young family now, it’s something else to balance.
“I have loved my time being captain and we have had a successful period and moulded a decent team with some good young players.
“Things are in good shape as is the club from the junior set-up all the way.
“Colin knows the club inside out and is a really experienced and well respected guy and it is good hands for the rest of the season.”
On his high points in charge, Baxter added: “There’s been lots of highlights.
“To come straight back up last year and win the Championship in the way we did was a highlight, especially after the disappointment of the previous year, as was winning the T20.”
Morley have enjoyed highs and lows in equal measure this term and are currently experiencing the latter with their weekend defeat at high-flying Hanging Heaton being their fourth on the spin.
The Tewits rallied from 19-3 to make 158-9, Dave Nebard taking 4-41 for Morley.
In reply, Morley were ripped apart by in-form spinner Muhammed Rameez, who took a stellar 6-9 as they were dismissed for just 51 leaving Heaton 27 points behind leaders Pudsey St Lawrence.
Morley’s experiences have been symptomatic of those endured by several sides this term, with only St Lawrence having showed true consistency.
Baxter added: “We have got three wins already and tied with Lightcliffe.
“When we stayed up last time around, we were bottom at half-way, having won just one game and then we won seven on the spin.
“It is just a funny league like that.”
Elsewhere, St Lawrence flexed their muscles in an outstanding 159-run win over Cleckheaton, which smacked of championship class.
Last season’s winners struck a powerhouse 293-4, with a typically accomplished opening stand of 119 arriving between Mark Robertshaw (74) and Adam Waite (55), with Barrie Frankland (44) and captain James Smith (65no) putting further meat on the knock.
Replying, Cleck were dismissed for just 124, Richie Lamb taking 5-51 with the Moorenders now dropping to a modest sixth spot.
A thriller saw third-placed Woodlands (199-8) edge out New Farnley (198-6) by just one run, despite the best efforts of Richard Atkins (60no) and James Middlebrook (48).
There was disappointment for Pudsey Congs (115), who lost out by 71 runs to East Bierley (186-9), Jonathon Donnelly taking 4-47 for the losers.
Scholes (106) lost out to Bradford and Bingley (108-6) with the weather intervening between Farsley (162-8) and Lightcliffe, stranded at 21-1 in reply.