South Shields seal signings of Gateshead and Spennymoor Town men
Baxter started his career with Newcastle United before going on to spend nine years over two spells at Gateshead, sandwiching by a one-year stay with Bedlington Terriers.
Cogdon, meanwhile, joins Shields after scoring the opener for Spennymoor in their Evo-Stik Division One North play-off final victory over Northwich Victoria.
The additions bring the number of arrivals so far this summer at Mariners Park to four, following the signings of David Palmer and Matthew Wade.
Baxter, 29, played at Mariners Park in February as part of the Gateshead side which was beaten 3-2 by Shields in the Durham Challenge Cup.
The right-back established himself as a popular figure at Gateshead during his time there, making well over 300 appearances for the club, including in the Conference play-off final of 2014.
He spent the 2012-13 season in the Northern League with Bedlington after being released by the Tynesiders, before returning to the Conference club a year later.
After being released by Gateshead again during this summer, he took time to consider his options, but has opted to make the move to Mariners Park.
He said: "I'm very happy to get everything sorted.
"I've been off since the end of April and have spoken to three or four clubs, and now I'm glad to get everything sorted so I know where I'll be playing next season.
"I met (chairman) Geoff Thompson and (manager) Jon King, and they told me about the club and the plans.
"If I'm honest, I could have stayed higher, but it was my decision to drop to this level with Shields and I'm convinced it's the right one. Hopefully it goes well and we can kick on this season."
Cogdon, meanwhile, has been a regular source of goals throughout his career, making his mark wherever he has been.
He is regarded extremely well at Spennymoor, with whom he won the FA Vase, Northern League and then the Evo-Stik Division One North play-off final last season.
The 33-year-old scored the opener at Wembley as Spennymoor won the FA Vase in 2013, beating Tunbridge Wells 2-1 in the final.
He is now looking forward to a new challenge at Shields after opting to leave Spennymoor in the summer.
The forward said: "I'm very pleased to join Shields, and am excited to get started.
"They were the first and only team I spoke to. When I spoke to Jon, there was only one team, really.
"It's the project. The pitch is getting done, and there are lots of plans with the ground.
"I got a good few calls from other clubs, but I said 'hang fire, because I'm going to speak to Shields', and once I had done that, there was no point in speaking to anyone else. This was the club I wanted to go to."
Manager Jon King was delighted by his latest two additions.
He said: "They are fantastic signings for the club.
"We've been speaking to them for a little while, and to get two players of their calibre in is brilliant for us.
"Craig brings energy and loads of experience, having played over 190 games in the Conference.
"To get him to the club and fight off competition from good sides is fantastic for us.
"He was a full-time footballer last season, and to get him shows the ambition of the club.
"I've known Gavin for years, and have seen him from the start of his career.
"He has been a legend at Spennymoor, and has still got the hunger.
"He's a great, infectious lad, and will bring us lots of positives in the final third of the pitch."