The micro-blogging site started testing the feature in Canada over the summer, before the United States and Japan in September, and it will now be available for everyone around the world.
In a statement, Twitter said: "Currently, repliers can shift the topic or tone of a discussion and derail what you and your audience want to talk about.
"To give you more control over the conversations you start, we tested the option for you to hide replies to your tweets."
The company found that most people using the feature removed replies which were "irrelevant, off-topic, or annoying".
Twitter's CEO Jack Dorsey recently declared that they are actively working on ways to "identify and remove abusive content".
The site has come under fire for not to doing enough to prevent trolling, but the co-founder reassured users that they are cracking down on the spreading of hateful messages.
He said: "We're continuing to improve relevance while testing ways to make it easier for people to find what they are looking for on Twitter.
"We also continue to make progress on health, improving our ability to proactively identify and remove abusive content, with more than 50% of the tweets removed for abusive content in Q3 taken down without a bystander or first person report."
One way they have done this is by launching a new filter to hide DMs (Direct Messages) containing malicious content.
The new tool appears in the Message Requests section of a user's inbox and it will be possible to delete any rogue messages.
Twitter previously vowed to "improve the health of conversation" after they were criticised by governments for not doing enough to prevent the spreading of hateful comments online.
Even the man who invented Twitter's retweet button compared it to "handing a four-year-old a loaded weapon".
Developer Chris Wetherell - who led the team to create the tool to share posts in 2009 - admitted that it has given the people the "power" to spread any kind of message.
He said: "We put power in the hands of the people.
"But now, what if you just say it slightly differently: Oh no, we put power into the hands of the people."
His admission came after Jack admitted the micro-blogging platform needed to do more to tackle online abuse.
The company supremo feels more needs to be done in order to combat abuse, conceding that putting the burden on victims to report abuse was not the way forward.
Asked what grade he would give himself for "tech responsibility", Dorsey said: "Myself? C.
"We've made progress but it has been scattered and not felt enough.
"And we've put most of the burden on the victims of abuse (that's a huge fail)."