The BHA announced a series of alterations to the regulations in the summer, with jockeys only allowed to use the whip in the backhand position and serious breaches to result in disqualification from races and possible 28-day bans for riders in major races.
However, further revisions were made to those plans after a number of riders registered their disquiet, with the implementation of the backhand-only rule proving a particularly unpopular prospect.
The BHA reversed its decision on banning the forehand position on Wednesday, but overall permitted use of the whip in races will be reduced and penalties will be made much stiffer, with 40-day suspensions a possibility for the worst offences in class one and two races.
Three-times Flat champion Moore is pleased to see the BHA and riders agree on a revised outcome.
In a statement issued by the Professional Jockeys Association, he said: "We thank the many well-intentioned individuals who have spent time on this issue. Horseracing must be competitive, have integrity and aim for the highest possible standards from all participants.
"I welcome the fact that the backhand-only rule has been discarded and that the BHA will continue to discuss and work with us in the future and hope that British racing and other jurisdictions will work together to find long-term solutions."
National Hunt jockey Tom Scudamore was part of the Whip Consultation Steering Group which drew up the new rules.
He added: "After the recent issues raised and consultations with the BHA board, through the PJA, I welcome the changes made.
"I hope that we can continue dialogue between both PJA and BHA to monitor the situation in order to maintain the highest standards that is expected every day in British racing."
Fellow jockey Tom Cannon believes the new regulations should be "fairly black and white now".
Flat riders will be allowed to strike their mounts six times in a race, with jump jockeys allowed seven uses of the whip - a compromise which Cannon feels is satisfactory when combined with tougher penalties.
He said: "They were pushing for us to use the backhand and it is what it is now. The forehand position looks better, it looks better to ride with, better for the horses, so hopefully common sense has prevailed. So, hopefully we can just get on with it now and concentrate on the racing.
"I was involved later on (with discussions) but not to begin with, like a lot of us were. A lot of us were not in the initial discussions, but it got a lot more serious and as time went on and we realised that they were coming in and a lot of us got involved.
"I think common sense has prevailed and while there will be a few bans dotted about, that is going to be the case whatever. We just have to concentrate on the racing now, which won't be affected.
"We said that using it in the backhand position was not great for the horses, as a lot of jockeys can't use it properly in that position and you are hitting them down the ribs a lot. That opens up a can of worms in itself.
"Losing one hit and getting stronger penalties takes the grey area out of it and it is fairly black and white now. Hopefully, it is something everyone can abide by and it is definitely an improvement on what they suggested first time around."
Charlie Deutsch reported the "majority" of riders to be happy with the changes and believes it should benefit their equine partners too.
He said: "I think it is a better way forward - just the technique is better, basically. And that makes it easier for jockeys to land the whip in the right place.
"With the backhand, you are more likely to get their ribs, instead of their rump. You want to be going for the fleshy backend, which is very important.
"It would have been a big old problem for a few years (if the proposed rules had not been changed), so all credit to the BHA for changing their minds so quickly, so we can get it done, move on and get some good publicity.
"If they have to do something, then they have to be harsh with the way it is going. The majority of the weighing room are happy. I just spoke to the lads towards the latter stages, but left it to the senior jockeys."
Sean Bowen incurred a four-day ban for his winning ride aboard Noble Yeats in the Many Clouds Chase at Aintree last month, when the stewards found he had hit his mount in the wrong place as he practiced his backhand whip use in the finish.
He said: "It is massive for me more than a lot of people, because I have always had a backhand issue, trying to get it all the way back you do find sometimes you are hitting the horse in the wrong place in the backhand, I've been trying to adapt myself - then the new rules came out last night. I got myself a ban for no reason whatsoever.
"Hitting them in the forehand is the correct way and the penalties go up at the same time, which is also correct."