Hampshire-based Onecom was the subject of 1,050 complaints, the Information Commissioner's Office (ICO) said.
The firm, based in Whiteley, is run by Aaron Brown. He was recently acquitted of the manslaughter of his friend who died in a powerboat crash in 2015.
ICO said Onecom could not provide evidence to explain the source of the data used to send the 1,050 messages.
It said the firm was also unable to prove it had consent to send the messages.
ICO said Onecom confirmed it had sent 3.3 million text messages between 1 October 2015 and 31 March 2016.
Steve Eckersley, ICO head of enforcement, said: "Spam texts are a real nuisance to millions of people across the country and this firm's failure to follow the rules drove over 1,000 people to complain."
Anyone bothered by a spam text is urged to report it, either via the ICO's website or by forwarding the text to 7726.
In March, Onecom chief executive Mr Brown was cleared of the manslaughter by gross negligence of Ryan McKinlay who died when a jet-powered boat, driven by Mr Brown, crashed into a cruiser off the Isle of Wight.

Images appeared to show Drissa Traore, Brandon Ormonde-Ottewill and Jeremy Balmy taking the legal high, commonly known as laughing gas, via balloons.
Swindon suspended the trio on 7 April and, following a club investigation, a statement said: "Swindon Town now consider this matter to be closed.
"The three first-team players have been fined for their actions."
The statement added: "The trio acknowledge that their actions were wrong and would like to apologise to their team mates, the club's staff and the supporters.
"They are keen to move on from this issue and get back to training to help the team as quickly as possible. All three will be considered for selection once again this weekend."
Head coach Luke Williams told BBC Wiltshire: "They will be available (on Saturday) because they will have served their suspension time but the boys will have to earn their right to be back in the matchday squad.
"I should think there's a level of conditioning that they've now lost because they have not been training for a fortnight, so they'll have to be re-conditioned.
"They'll have to show in training every day that they're desperately trying to make up for what they've done."
Swindon host Chesterfield in League One on Saturday.
A telecoms firm has been fined Â£100,000 for sending millions of spam texts about mobile phone upgrades.
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Swindon Town have fined three players after they appeared to inhale nitrous oxide in a live social media video.