Those wanting to sign up need to text 'TPS' followed by their email address to the shortcode 78070. They will receive a text reply from the TPS confirming their number has been successfully added to its database.
Registrants should notice a gradual reduction in unsolicited sales and marketing voice calls after a few days, although it can take up to 28 days for the service to become fully effective.
It is illegal for organisations to make unsolicited sales and marketing calls to numbers registered with the TPS, unless they have a person's consent to do so.
Only 48 per cent of people familiar with the TPS are aware that mobile numbers can be registered, compared to 88 per cent for landline phone numbers, according to Ofcom.
The regulator said this helped to explain why only 2.9 million mobile numbers (around 3 per cent) were registered on the TPS database, compared with 18.5 million landline numbers (around 85 per cent).
John Mitchison, head of the TPS, said: "Rogue callers operate illegally and against the interests of ordinary people.
"Texting will make it easier for people to register their mobile numbers on the TPS, which is the only official no-call list, and help us stamp out rogue callers once and for all by giving the Information Commissioner more ammunition to prosecute these cases."