John has come through the region's ranks and earned his spurs playing Principality Premiership rugby with Aberavon, while Arhip has travelled from far further afield having left his native Moldova for Romania and then Russia prior to heading to Wales in November 2012.
The region have high hopes for the duo, with rugby operations manager Andy Lloyd convinced that they can be an integral part of the Ospreys' long-term progress.
"It's very good news that a local, young talent like Ben will remain with us for the next two years. He has really made a big breakthrough since the start of last year and has started to show the wider Ospreylian public what we already knew here, which is that he can grow to be an influential figure in midfield," said Lloyd.
"His early senior experiences with us saw him playing a lot on the wing but that accelerated his development and understanding of what we are trying to do as a back line and where we want to take our game over the next few seasons.
"We have in place a strong group of backs, all of a similar age, that have come through our development system and want to achieve great things in an Ospreys shirt. With the right support, on and off the field, they can really help to make this region stronger.
"Dmitri was a fantastic find for us as supporters saw last season and he has the potential to become a key player for the region. He is an amazing athlete and once we get him back up to full fitness he will be a real asset for us.
"He has a great attitude, is diligent, and is always looking to learn. His versatility means he offers real value, as he can play right across the front row. He has a little bit to learn but we see him really adding depth to our pool of tight heads while providing valuable cover elsewhere. He has a very bright future as an Osprey."
Arhip hasn't featured since pre-season after rupturing his Achilles in August but he made enough of a positive impression in nine games last term to secure a new deal. This season has proved more fruitful for 23-year-old John, with the former Wales U20 star featuring 17 times so far to take his Ospreys tally to 33, but he too is currently sidelined with a shoulder problem he picked up in the Heineken Cup defeat at Leinster in January.
No date has yet been set for Arhip's return to action - the 25-year-old admits 'it may be one month, it may be two months or it may be next season' - but John is targeting a comeback in the final month of the current campaign as the Ospreys go in search of a fifth RaboDirect PRO12 title.