Blake, a former Wales international, has been without a club since being released by Crystal Palace in January, while Feely has arrived on loan from Charlton.
Both will remain with the League Two club until the end of the season and could feature at the weekend against Torquay.
Blake, who has 14 caps for Wales, told the club's official website: "I had been training with Birmingham City since February but am grateful for Justin Edinburgh and Newport County AFC in showing faith and signing me through until the end of the season.
"I can't wait to get started and playing games for the County. There is plenty to play for in these last 10 games and I am hoping to be involved at Torquay on Saturday."
Feely, who has had a stint at AFC Wimbledon this year, added: "It's all been a bit of a whirlwind. I got the call from Charlton yesterday afternoon and by 8:00pm I was on the road to south Wales.
"I just want to play games and I spoke to (former Charlton team-mate) Michael Smith who was really positive about his time there and told me the squad and staff are a good bunch of lads."