Former Rangers defender Hutton 26, has agreed a permanent move to Villa Park, signing a contract through to 2015 while Jenas has joined on loan for the rest of the season.
A statement on Villa's website from manager Alex McLeish said: "Alan is a player whom I know well. He is an athletic full-back in his mid-20s - a very good age - and he has a lot of experience playing at a high level, both internationally with Scotland and with Rangers and Tottenham which are big clubs. So he fits the bill in terms of having the right temperament to be an important and influential player for Villa.
"Jermaine is a dynamic midfield player and I feel he will add to the quality of the squad as well. He also has played at a very high level and I'm sure he will be relishing this opportunity."
Villa earlier confirmed they reached an agreement with Shamrock Rovers to sign Republic of Ireland Under-21 international defender Enda Stevens in January. Stevens, 21, was part of the team that beat Partizan Belgrade to reach the UEFA Europa League group stages and will remain with Shamrock until the new year.
He said: "This is massive for me. It's a dream come true. I never expected it to come as soon as it has, especially after the last few games in Europe. I grew up following and watching the Premier League and I can dream of playing in it now. Villa have had some great Irish players and been very good for Irish players. I'm a player who likes to get forward, can defend and I like to play football. I like to get the ball down and play."