The Guinness Book of Records has yet to confirm whether the feat will make it into the record books.
The east London-based brother of Kim Sears was pulling a sled weighing around 100kg containing all his food, fuel and equipment, and he was burning approximately 10,000 calories per day.
He covered the distance without help or resupply, but he said the term solo is "incredibly misleading".
"'Absolutely could not have done this without the help of my co-presenting sponsors The Shackleton Company and Juice Plus. Both have been instrumental in equipping and preparing me for this expedition."
On the penultimate day, Lt Sears said only snacks and music on his iPod kept him going after he found it hard to go on.
He wrote: "I couldn't have asked for better weather but well and truly hit a wall midway through the day. I wanted to make sure I was under 30km from the pole for a good finish tomorrow. At 38km left to go I hit the wall, I've never experienced anything like it, I would take a couple of steps and just stop, everything was just saying 'no more, not one more step'.
"I'm not sure what is more surreal, the fact I'm so close to finally reaching the pole or that the shortbread and pepperamis I bought from Asda in Shoreditch are still acceptable to eat after opening them at the start of November!"
Lt Sears has raised more than £33,500, above his original £25,000 target, for the Gurkha Welfare Trust to help rebuild schools in Gorkha, Nepal, destroyed in the earthquake of April 2015.