Oscar, aged 14, was reported missing having last been seen at an address in Corfe Mullen at around 5pm on Wednesday March 25.
He is believed to be in the company of Lottie, aged 16, who was also reported missing after leaving an address in Weymouth at around 9:20pm on Wednesday March 25.
They are believed to have been in the Weymouth area and may have also travelled to Dorchester and Poole.
Lottie was wearing a grey hooded top, black leggings or tracksuit bottoms and white trainers. Oscar was wearing a grey and black tracksuit with a black hood and predominantly grey tracksuit bottoms.
Officers who are searching for the two missing teenagers are now appealing for information from the public to help find them.
Chief inspector Ashley Smith, of Dorset Police, said: “We are concerned for the welfare of these two young individuals and are carrying out searches to locate them, as we just want to make sure they are all right.
“I would urge anyone who has any information regarding their whereabouts to please contact us immediately.
“I would also like to appeal directly to Oscar and Lottie to please get in touch with us or your loved ones and let us know where you are. We just want to check that you are OK.”
Anyone with information or knowledge as to Oscar and Lottie’s whereabouts is asked to contact Dorset Police online or by calling 999, quoting occurrence number 55260042491.